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A165259 Sum of odd powers of 4 and 9 divided by 13. 2
1, 61, 4621, 369181, 29821741, 2414250301, 195533302861, 15837861987421, 1282861452271981, 103911691734684541, 8416845656119913101, 681764476155480405661, 55222922216750191970221 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
Sequence in context: A096544 A242230 A201031 * A181636 A167736 A015288
KEYWORD
nonn
AUTHOR
Jaume Oliver Lafont, Sep 11 2009
STATUS
approved

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Last modified June 14 07:34 EDT 2024. Contains 373393 sequences. (Running on oeis4.)