A152257 a(n) = (3^n - 1)^2*(3^n + 1)/16.

0, 1, 40, 1183, 32800, 893101, 24180520, 653473003, 17649155200, 476575627801, 12867977828200, 347439324082423, 9380897054183200, 253284538196972101, 6838685390919695080, 184644531291230453443, 4985402576490767372800, 134605871649898496094001

Offset: 0

Author

Roger L. Bagula, Dec 01 2008

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 0..698
• Index entries for linear recurrences with constant coefficients, signature (40,-390,1080,-729).

Crossrefs

Cf. A002452, A003462, A007051, A238976.

Programs

Magma

[(9^n-1)*(3^n-1)/16: n in [0..40]]; // G. C. Greubel, May 22 2023

Maple

seq((3^n-1)^2*(3^n+1)/16,n=0..30); # Robert Israel, Mar 18 2019

Mathematica

Table[(9^n-1)*(3^n-1)/16, {n,0,30}]

PARI

concat(0, Vec(x*(1 - 27*x^2) / ((1 - x)*(1 - 3*x)*(1 - 9*x)*(1 - 27*x)) + O(x^20))) \\ Colin Barker, Mar 18 2019

SageMath

[(9^n-1)*(3^n-1)//16 for n in range(41)] # G. C. Greubel, May 22 2023

Formula

a(n) = (3^n - 1)*(3^n - 1)*(3^n + 1)/16.

G.f.: x*(1-27*x^2)/((1-x)*(1-3*x)*(1-9*x)*(1-27*x)). - Robert Israel, Mar 18 2019

a(n) = 40*a(n-1) - 390*a(n-2) + 1080*a(n-3) - 729*a(n-4) for n>3. - Colin Barker, Mar 18 2019

From G. C. Greubel, May 22 2023: (Start)

a(n) = A002452(n)*A003462(n).

a(n) = A007051(n)*A238976(n+1)/2.

E.g.f.: (1/16)*(exp(x) - exp(3*x) - exp(9*x) + exp(27*x)). (End)

Extensions

0 inserted by Robert Israel, Mar 18 2019