A005897 -id:A005897

A019456

Coordination sequence T1 for Zeolite Code CZP.

+10
3

1, 4, 9, 18, 32, 54, 83, 113, 149, 191, 234, 281, 342, 399, 459, 537, 611, 678, 763, 861, 947, 1035, 1151, 1267, 1367, 1481, 1611, 1738, 1862, 1995, 2140, 2291, 2443, 2591, 2751, 2929, 3094, 3252, 3439, 3639, 3816, 3995, 4211, 4427, 4618, 4823, 5055

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

REFERENCES

W. M. Meier, D. H. Olson and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996

LINKS

R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000

R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences

R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.

Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane

International Zeolite Association, Database of Zeolite Structures

CROSSREFS

Cf. A019457, A019458.

KEYWORD

nonn

AUTHOR

Ralf W. Grosse-Kunstleve

STATUS

approved

A019457

Coordination sequence T2 for Zeolite Code CZP.

+10
3

1, 4, 10, 20, 33, 56, 85, 114, 144, 192, 242, 280, 333, 412, 475, 526, 602, 698, 776, 850, 949, 1058, 1157, 1258, 1372, 1500, 1620, 1732, 1863, 2020, 2161, 2280, 2434, 2624, 2778, 2910, 3087, 3294, 3463, 3618, 3818, 4038, 4228, 4410, 4625, 4864, 5075

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

REFERENCES

W. M. Meier, D. H. Olson and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996

LINKS

R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000

R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences

R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.

Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane

International Zeolite Association, Database of Zeolite Structures

CROSSREFS

Cf. A019456, A019458.

KEYWORD

nonn

AUTHOR

Ralf W. Grosse-Kunstleve

STATUS

approved

A019458

Coordination sequence T3 for Zeolite Code CZP.

+10
3

1, 4, 8, 16, 33, 52, 73, 112, 160, 190, 214, 282, 351, 386, 439, 548, 624, 658, 742, 872, 953, 1012, 1127, 1276, 1380, 1462, 1582, 1744, 1877, 1970, 2101, 2302, 2464, 2558, 2710, 2948, 3113, 3210, 3397, 3660, 3834, 3952, 4166, 4444, 4637, 4782, 5005

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

REFERENCES

W. M. Meier, D. H. Olson and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996

LINKS

R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000

R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences

R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.

Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane

International Zeolite Association, Database of Zeolite Structures

CROSSREFS

Cf. A019456, A019457.

KEYWORD

nonn

AUTHOR

Ralf W. Grosse-Kunstleve

STATUS

approved

A033616

Coordination sequence T1 for Zeolite Code TSC.

+10
3

1, 4, 9, 16, 25, 37, 53, 74, 99, 125, 151, 177, 205, 238, 279, 328, 381, 434, 483, 528, 574, 627, 690, 762, 840, 919, 995, 1068, 1140, 1214, 1294, 1382, 1477, 1577, 1681, 1787, 1892, 1995, 2096, 2197, 2303, 2419, 2546, 2681, 2819, 2954, 3082, 3205, 3329

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

First 127 terms computed by Davide M. Proserpio using ToposPro.

LINKS

R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000(terms 0..127 from Davide M. Proserpio)

V. A. Blatov, A. P. Shevchenko, D. M. Proserpio, Applied Topological Analysis of Crystal Structures with the Program Package ToposPro, Cryst. Growth Des. 2014, 14, 3576-3586.

R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences

Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane

International Zeolite Association, Database of Zeolite Structures

Reticular Chemistry Structure Resource (RCSR), The tsc tiling (or net)

FORMULA

G.f.: (1 + x)^3 * (1 + x^2) * (1 - x + 2*x^2 - x^3 + 3*x^4 - x^5 + 4*x^6 - x^7 + 4*x^8 - x^9 + 4*x^10 - x^11 + 4*x^12 - x^13 + 3*x^14 - x^15 + 2*x^16 - x^17 + x^18) / ((1 - x)^3 * (1 - x + x^2 - x^3 + x^4) * (1 + x + x^2 + x^3 + x^4) * (1 + x^3 + x^6) * (1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). - Colin Barker, Dec 19 2015

From N. J. A. Sloane, Feb 22 2018 (Start)

The following is a another conjectured recurrence, found by gfun, using the command rec:=gfun[listtorec](t1, a(n)); (where t1 is a list of the initial terms) suggested by Paul Zimmermann.

Note: this should not be used to extend the sequence.

0 = (-38*n^3-836*n^2-5351*n)*a(n)+(-76*n^2-798*n)*a(n+1)+(-38*n^3-912*n^2-6149*n)*a(n+2)+(-38*n^3-988*n^2-6947*n)*a(n+3)+(-38*n^3-1064*n^2-7745*n)*a(n+4)+(-38*n^3-1140*n^2 -8543*n)*a(n+5)+(-76*n^3-2052*n^2-14692*n)*a(n+6)

+ (-532*n^2-5586*n)*a(n+7)+(-76*n^3-2204*n^2-16288*n)*a(n+8)+(-684*n^2-7182*n)*a(n+9)+(-684*n^2 -7182*n)*a(n+10)+(-684*n^2-7182*n)*a(n+11)+(-684*n^2-7182*n)*a(n+12)+(76*n^3+ 988*n^2+3520*n)*a(n+13)+(-532*n^2-5586*n)*a(n+14)+(76*n^3+1140*n^2+5116*n)*a(n+15)

+ (38*n^3+456*n^2+1361*n)*a(n+16)+(38*n^3+532*n^2+2159*n)*a(n+17)+(38*n^3+608*n^2+2957*n)*a(n+18)+(38*n^3+684*n^2+3755*n)*a(n+19)+(-76*n^2-798*n)*a(n+20)+(38*n^3+760*n^2+4553*n)*a(n+21), with

a(0) = 1, a(1) = 4, a(2) = 9, a(3) = 16, a(4) = 25, a(5) = 37, a(6) = 53, a(7) = 74, a(8) = 99, a(9) = 125, a(10) = 151, a(11) = 177, a(12) = 205, a(13) = 238, a(14) = 279, a(15) = 328, a(16) = 381, a(17) = 434, a(18) = 483, a(19) = 528, a(20) = 574, a(21) = 627

(End)

CROSSREFS

Cf. A033617 (second type), A299902 (partial sums).

KEYWORD

nonn

AUTHOR

Ralf W. Grosse-Kunstleve

STATUS

approved

A033617

Coordination sequence T2 for Zeolite Code TSC.

+10
3

1, 4, 9, 17, 28, 41, 56, 73, 93, 117, 146, 180, 216, 253, 291, 329, 369, 414, 466, 524, 586, 650, 712, 773, 836, 902, 973, 1051, 1136, 1224, 1313, 1403, 1492, 1581, 1673, 1769, 1870, 1978, 2093, 2211, 2329, 2447, 2563, 2678, 2797, 2923, 3057, 3198, 3344

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

First 127 terms computed by Davide M. Proserpio using ToposPro.

LINKS

R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000 (terms 0..127 from Davide M. Proserpio)

V. A. Blatov, A. P. Shevchenko, and D. M. Proserpio, Applied Topological Analysis of Crystal Structures with the Program Package ToposPro, Crystal Growth & Design, Vol. 14, No. 7 (2014), 3576-3586.

R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences

Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane

International Zeolite Association, Database of Zeolite Structures

Reticular Chemistry Structure Resource (RCSR), The tsc tiling (or net)

FORMULA

G.f.: (1 + x)^3 * (1 - x + x^2) * (1 + x^2) * (1 + x^2 + x^3 + x^4 + x^5 + 2*x^6 + x^7 + 3*x^8 + x^9 + 2*x^10 + x^11 + x^12 + x^13 + x^14 + x^16) / ((1 - x)^3 * (1 - x + x^2 - x^3 + x^4) * (1 + x + x^2 + x^3 + x^4) * (1 + x^3 + x^6) * (1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). - Colin Barker, Dec 20 2015

From N. J. A. Sloane, Feb 22 2018 (Start)

The following is another conjectured recurrence, found by gfun, using the command rec:=gfun[listtorec](t1, a(n)); (where t1 is a list of the initial terms) suggested by Paul Zimmermann.

Note: this should not be used to extend the sequence.

0 = (-38*n^3-836*n^2-5367*n)*a(n)+(-76*n^2-798*n)*a(n+1)+(-38*n^3-912*n^2-6165*n)*a(n+2)+(-38*n^3-988*n^2-6963*n)*a(n+3)+(-38*n^3-1064*n^2-7761*n)*a(n+4)+(-38*n^3-1140*n^2-8559*n)*a(n+5)+(-76*n^3-2052*n^2-14724*n)*a(n+6)

+ (-532*n^2-5586*n)*a(n+7)+(-76*n^3-2204*n^2-16320*n)*a(n+8)+(-684*n^2-7182*n)*a(n+9)+(-684*n^2-7182*n)*a(n+10)+(-684*n^2-7182*n)*a(n+11)+(-684*n^2-7182*n)*a(n+12)+(76*n^3+988*n^2+3552*n)*a(n+13)+(-532*n^2-5586*n)*a(n+14)

+ (76*n^3+1140*n^2+5148*n)*a(n+15)+(38*n^3+456*n^2+1377*n)*a(n+16)+(38*n^3+532*n^2+2175*n)*a(n+17)+(38*n^3+608*n^2+2973*n)*a(n+18)

+ (38*n^3+684*n^2+3771*n)*a(n+19)+(-76*n^2-798*n)*a(n+20)+(38*n^3+760*n^2+4569*n)*a(n+21), with

a(0) = 1, a(1) = 4, a(2) = 9, a(3) = 17, a(4) = 28, a(5) = 41, a(6) = 56, a(7) = 73, a(8) = 93, a(9) = 117, a(10) = 146, a(11) = 180, a(12) = 216, a(13) = 253, a(14) = 291, a(15) = 329, a(16) = 369, a(17) = 414, a(18) = 466, a(19) = 524, a(20) = 586, a(21) = 650.

(End)

CROSSREFS

Cf. A033616, A299903 (partial sums).

KEYWORD

nonn

AUTHOR

Ralf W. Grosse-Kunstleve

STATUS

approved

A008016

Coordination sequence T2 for Zeolite Code AFO.

+10
2

1, 4, 11, 22, 41, 65, 88, 111, 145, 186, 231, 281, 336, 395, 455, 518, 597, 679, 752, 827, 921, 1024, 1123, 1222, 1330, 1442, 1555, 1678, 1821, 1965, 2088, 2207, 2357, 2518, 2671, 2829, 2996, 3167, 3335, 3506, 3705, 3903, 4072, 4247, 4461, 4688, 4899, 5104

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

REFERENCES

W. M. Meier, D. H. Olson and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996

LINKS

R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000

R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences

R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.

Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane

International Zeolite Association, Database of Zeolite Structures

KEYWORD

nonn

AUTHOR

Ralf W. Grosse-Kunstleve

STATUS

approved

A008040

Coordination sequence T3 for Zeolite Code ATS.

+10
2

1, 4, 10, 19, 32, 51, 72, 96, 124, 155, 196, 238, 278, 324, 374, 436, 500, 558, 620, 688, 772, 857, 934, 1014, 1098, 1203, 1310, 1405, 1504, 1606, 1730, 1858, 1972, 2089, 2210, 2355, 2502, 2634, 2770, 2909, 3076, 3244, 3392, 3546, 3704, 3892, 4082, 4248

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

REFERENCES

W. M. Meier, D. H. Olson and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996

LINKS

R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000

R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences

R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.

Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane

International Zeolite Association, Database of Zeolite Structures

FORMULA

G.f.: (1 + x) * (1 + 2*x + 5*x^2 + 7*x^3 + 13*x^4 + 16*x^5 + 18*x^6 + 20*x^7 + 18*x^8 + 16*x^9 + 13*x^10 + 7*x^11 + 5*x^12 + 2*x^13 + x^14) / ((1 - x)^3 * (1 - x + x^2) * (1 + x + x^2) * (1 + x + x^2 + x^3 + x^4)^2). - Colin Barker, Dec 21 2015

KEYWORD

nonn

AUTHOR

Ralf W. Grosse-Kunstleve

STATUS

approved

A008148

Coordination sequence T3 for Zeolite Code MEI.

+10
2

1, 4, 10, 16, 26, 46, 66, 94, 114, 158, 194, 222, 262, 334, 384, 404, 464, 564, 634, 670, 748, 826, 934, 1002, 1092, 1160, 1280, 1378, 1504, 1566, 1710, 1816, 1956, 2024, 2206, 2328, 2464, 2542, 2748, 2876, 3052, 3132, 3364, 3492, 3688, 3798, 4028, 4152

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

REFERENCES

W. M. Meier, D. H. Olson and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996.

LINKS

R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000

R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences

R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.

Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane

International Zeolite Association, Database of Zeolite Structures

KEYWORD

nonn

AUTHOR

Ralf W. Grosse-Kunstleve

STATUS

approved

A008185

Coordination sequence T4 for Zeolite Code MOR.

+10
2

1, 4, 11, 24, 39, 60, 92, 122, 148, 195, 250, 293, 342, 403, 472, 551, 621, 690, 786, 879, 954, 1047, 1168, 1293, 1397, 1484, 1622, 1773, 1880, 2007, 2181, 2336, 2456, 2606, 2783, 2966, 3122, 3278, 3468, 3672, 3855, 4037, 4253, 4466, 4664, 4853, 5081, 5338

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

REFERENCES

W. M. Meier, D. H. Olson and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996.

LINKS

R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000

R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences

R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.

Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane

International Zeolite Association, Database of Zeolite Structures

KEYWORD

nonn

AUTHOR

Ralf W. Grosse-Kunstleve

STATUS

approved

A008242

Coordination sequence T2 for Zeolite Code TON.

+10
2

1, 4, 12, 23, 43, 66, 91, 128, 169, 214, 258, 306, 381, 450, 509, 574, 659, 771, 848, 924, 1038, 1148, 1274, 1373, 1491, 1636, 1743, 1902, 2051, 2188, 2340, 2466, 2689, 2864, 2991, 3170, 3343, 3611, 3776, 3910, 4166, 4362, 4626, 4813, 5007, 5296, 5461, 5768

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

REFERENCES

W. M. Meier, D. H. Olson and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996

LINKS

R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000

R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences

R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.

Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane

International Zeolite Association, Database of Zeolite Structures

KEYWORD

nonn

AUTHOR

Ralf W. Grosse-Kunstleve

STATUS

approved