A074507 a(n) = 1^n + 3^n + 5^n.

3, 9, 35, 153, 707, 3369, 16355, 80313, 397187, 1972809, 9824675, 49005273, 244672067, 1222297449, 6108298595, 30531927033, 152630937347, 763068593289, 3815084686115, 19074648589593, 95370918425027, 476847618556329

Offset

0,1

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

T. A. Gulliver, Divisibility of sums of powers of odd integers, Int. Math. For. 5 (2010) 3059-3066, eq. (6).

D. Suprijanto, I. W. Suwarno, Observation on Sums of Powers of Integers Divisible by 3k-1, Applied Mathematical Sciences, Vol. 8, 2014, no. 45, 2211 - 2217.

Index entries for linear recurrences with constant coefficients, signature (9,-23,15).

Formula

a(n) = 8*a(n-1) - 15*a(n-2) + 8.

G.f.: 1/(1-x)+1/(1-3*x)+1/(1-5*x). E.g.f.: e^x+e^(3*x)+e^(5*x). [Mohammad K. Azarian, Dec 26 2008]

Mathematica

Table[1^n + 3^n + 5^n, {n, 0, 22}]
LinearRecurrence[{9, -23, 15}, {3, 9, 35}, 30] (* Harvey P. Dale, Mar 02 2022 *)

Prog

(PARI) a(n) = 1 + 3^n + 5^n; \\ Michel Marcus, Aug 07 2017

Crossrefs

Cf. A001550, A001576, A034513, A001579, A074501-A074580.

Sequence in context: A225041 A335642 A327885 * A217924 A030268 A097277

Adjacent sequences: A074504 A074505 A074506 * A074508 A074509 A074510

Keyword

easy,nonn

Author

Robert G. Wilson v, Aug 23 2002

Status

approved