OFFSET
0,2
COMMENTS
Sum of n-th octagonal number and n-th 9-gonal (nonagonal) number.
Sum of reciprocals of a(n), for n>0: 0.629618994194109711163742089971688...
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: x*(2+11*x)/(1-x)^3.
a(n) + a(-n) = A152742(n).
a(0)=0, a(1)=2, a(2)=17; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Jun 19 2013
E.g.f.: x*(4 + 13*x)*exp(x)/2. - G. C. Greubel, Aug 30 2019
MAPLE
MATHEMATICA
Table[n(13n-9)/2, {n, 0, 50}]
LinearRecurrence[{3, -3, 1}, {0, 2, 17}, 50] (* Harvey P. Dale, Jun 19 2013 *)
CoefficientList[Series[x(2+11x)/(1-x)^3, {x, 0, 45}], x] (* Vincenzo Librandi, Aug 18 2013 *)
PROG
(Magma) [n*(13*n-9)/2: n in [0..50]];
(Magma) I:=[0, 2, 17]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2) +Self(n-3): n in [1..50]]; // Vincenzo Librandi, Aug 18 2013
(PARI) a(n)=n*(13*n-9)/2 \\ Charles R Greathouse IV, Sep 24 2015
(Sage) [n*(13*n-9)/2 for n in (0..50)] # G. C. Greubel, Aug 30 2019
(GAP) List([0..50], n-> n*(13*n-9)/2); # G. C. Greubel, Aug 30 2019
CROSSREFS
Cf. numbers of the form n*(n*k-k+4)/2 listed in A005843 (k=0), A000096 (k=1), A002378 (k=2), A005449 (k=3), A001105 (k=4), A005476 (k=5), A049450 (k=6), A218471 (k=7), A002939 (k=8), A062708 (k=9), A135706 (k=10), A180223 (k=11), A139267 (n=12), this sequence (k=13), A139268 (k=14), A226489 (k=15), A139271 (k=16), A180232 (k=17), A152995 (k=18), A226490 (k=19), A152965 (k=20), A226491 (k=21), A152997 (k=22).
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Jun 09 2013
STATUS
approved