A152256 a(n) = (3^n - 1)*(3^n + 1)^2/32.

0, 1, 25, 637, 16810, 450241, 12123475, 327035437, 8827268020, 238312027681, 6434206838125, 173721623357437, 4690466178937630, 126642427965100321, 3419344125259375975, 92322278513810982637, 2492701404059145489640, 67302936867273104276161

Offset: 0

Author

Roger L. Bagula, Dec 01 2008

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..695
• Index entries for linear recurrences with constant coefficients, signature (40,-390,1080,-729).

Crossrefs

Cf. A002452, A003462, A007051, A051500.

Programs

Magma

[(9^n-1)*(3^n+1)/32: n in [0..40]]; // G. C. Greubel, May 22 2023

Mathematica

Table[(9^n-1)*(3^n+1)/32, {n,0,30}]

SageMath

[(9^n-1)*(3^n+1)/32 for n in range(41)] # G. C. Greubel, May 22 2023

Formula

a(n) = (3^n - 1)*(3^n + 1)^2/32.

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

a(n) = A002452(n)*A007051(n)/2.

a(n) = A003462(n)*A051500(n)/4.

G.f.: x*(1 -15*x +27*x^2)/((1-x)*(1-3*x)*(1-9*x)*(1-27*x)).

E.g.f.: (1/32)*(- exp(x) - exp(3*x) + exp(9*x) + exp(27*x)). (End)