A134006 a(n) = 1^n + 3^n + 5^n + 7^n.

4, 16, 84, 496, 3108, 20176, 134004, 903856, 6161988, 42326416, 292299924, 2026332016, 14085959268, 98111307856, 684331371444, 4778093436976, 33385561506948, 233393582580496, 1632228682596564, 11417969833962736

Offset: 0

Author

Artur Jasinski, Oct 01 2007

Keywords

• nonn

Examples

			a(3)=84 because 1^2+3^2+5^2+7^2=84.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• T. A. Gulliver, Divisibility of sums of powers of odd integers, Int. Math. For. 5 (2010) 3059-3066, eq. 6.
• Index entries for linear recurrences with constant coefficients, signature (16, -86, 176, -105).

Crossrefs

Cf. A034472, A074507, A134007.

Programs

Magma

[1^n + 3^n + 5^n + 7^n: n in [0..30]]; // Vincenzo Librandi, Jun 20 2011

Mathematica

Table[1^n+3^n+5^n+7^n,{n,0,30}]

PARI

{a(n) = 1^n + 3^n + 5^n + 7^n}; /* Michael Somos, Jun 29 2017 */

Formula

a(n) = 15*a(n-1) - 71*a(n-2) + 105*a(n-3) - 48.

a(n) = A074507(n) + A000420(n). - Michel Marcus, Nov 07 2013

G.f.: 1 / (1 - x) + 1 / (1 - 3*x) + 1 / (1 - 5*x) + 1 / (1 - 7*x), E.g.f.: exp(x) + exp(3*x) + exp(5*x) + exp(7*x). - Michael Somos, Jun 29 2017