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

Author

Jaume Oliver Lafont, Sep 11 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..520
• Index entries for linear recurrences with constant coefficients, signature (97,-1296).

Crossrefs

Cf. A007689, A082101, A096951.

Programs

Magma

[(4^(2*n+1)+9^(2*n+1))/13: n in [0..30]]; // 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 *)

PARI

a(n)=(4^(2*n+1)+9^(2*n+1))/13

SageMath

[(4^(2*n+1)+9^(2*n+1))/13 for n in range(31)] # G. C. Greubel, Mar 11 2023

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