The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A078010

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A078010

Expansion of (1-x)/(1 - x - x^2 - 2*x^3).
(history; published version)

#46 by N. J. A. Sloane at Fri Sep 01 04:23:52 EDT 2023

STATUS

proposed

approved

#45 by Andrew Howroyd at Thu Aug 31 12:37:31 EDT 2023

STATUS

editing

proposed

#44 by Andrew Howroyd at Thu Aug 31 12:37:03 EDT 2023

COMMENTS

For n > 0, a(n) is the number of ways to tile a strip of length n with squares, dominoes, and two colors of trominoes, with the restriction that the first tile can not cannot be a square. - _Greg Dresden _ and Bora Bursalı, Aug 31 2023

STATUS

proposed

editing

Discussion

Thu Aug 31

12:37

Andrew Howroyd: Corrected signature; can not -> cannot.

#43 by Greg Dresden at Thu Aug 31 12:28:38 EDT 2023

STATUS

editing

proposed

#42 by Greg Dresden at Thu Aug 31 12:28:34 EDT 2023

COMMENTS

For n > 0, a(n) is the number of ways to tile a strip of length n with squares, dominoes, and two colors of trominoes, with the restriction that the first tile can not be a square. - Greg Dresden and Bora Bursalı, Aug 31 2023

STATUS

approved

editing

#41 by Charles R Greathouse IV at Thu Sep 08 08:45:08 EDT 2022

PROG

(MAGMAMagma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1-x)/(1-x-x^2-2*x^3) )); // G. C. Greubel, Jun 28 2019

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#40 by Michael Somos at Wed Nov 18 14:57:35 EST 2020

STATUS

editing

approved

#39 by Michael Somos at Wed Nov 18 14:56:53 EST 2020

FORMULA

G.f.: (1 - x) / ((1 - 2*x) * (1 + x + x^2)). - Michael Somos, Nov 18 2020

EXAMPLE

a(6) = 19 = A077947(4) + 2*A077947(3) = 9 + 2*5 = 19.

G.f. = 1 + x^2 + 3*x^3 + 4*x^4 + 9*x^5 + 19*x^6 + 36*x^7 + 73*x^8 + ... - Michael Somos, Nov 18 2020

PROG

(PARI) {a(n) = ([0, 1, 1; 1, 1, 0; 0, 2, 0]^n)[1, 1]}; /* Michael Somos, Nov 18 2020 */

CROSSREFS

Cf. A033138, A077947.

STATUS

approved

editing

Discussion

Wed Nov 18

14:57

Michael Somos: Added more info. I added comment in A033138 also.

#38 by Joerg Arndt at Thu Jan 09 03:59:17 EST 2020

STATUS

reviewed

approved

#37 by G. C. Greubel at Mon Dec 30 15:28:48 EST 2019

STATUS

proposed

reviewed