A165259 Sum of odd powers of 4 and 9 divided by 13.

1, 61, 4621, 369181, 29821741, 2414250301, 195533302861, 15837861987421, 1282861452271981, 103911691734684541, 8416845656119913101, 681764476155480405661, 55222922216750191970221

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..520

Index entries for linear recurrences with constant coefficients, signature (97,-1296).

Formula

G.f.: (1-36*x)/((1-16*x)*(1-81*x))

a(n) = 97*a(n-1) - 1296*a(n-2). - Harvey P. Dale, Jun 23 2013

E.g.f.: (1/13)*(4*exp(16*x) + 9*exp(81*x)). - G. C. Greubel, Mar 11 2023

Mathematica

Table[(4^n+9^n)/13, {n, 1, 31, 2}] (* or *) LinearRecurrence[{97, -1296}, {1, 61}, 20] (* Harvey P. Dale, Jun 23 2013 *)

Prog

(PARI) a(n)=(4^(2*n+1)+9^(2*n+1))/13
(Magma) [(4^(2*n+1)+9^(2*n+1))/13: n in [0..30]]; // G. C. Greubel, Mar 11 2023
(SageMath) [(4^(2*n+1)+9^(2*n+1))/13 for n in range(31)] # G. C. Greubel, Mar 11 2023

Crossrefs

Cf. A007689, A082101, A096951.

Sequence in context: A096544 A242230 A201031 * A181636 A167736 A015288

Adjacent sequences: A165256 A165257 A165258 * A165260 A165261 A165262

Keyword

nonn

Author

Jaume Oliver Lafont, Sep 11 2009

Status

approved