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
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).
Programs
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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 *) -
PARI
a(n) = 1 + 3^n + 5^n; \\ Michel Marcus, Aug 07 2017
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]