A134007 a(n) = 1^n + 3^n + 5^n + 7^n + 9^n.

5, 25, 165, 1225, 9669, 79225, 665445, 5686825, 49208709, 429746905, 3779084325, 33407391625, 296515495749, 2639977136185, 23561123826405, 210669225531625, 1886405750358789, 16910575282247065, 151726863979595685

Offset: 0

Author

Artur Jasinski, Oct 01 2007

Keywords

• nonn
• easy

Examples

			a(3)=165 because 1^2 + 3^2 + 5^2 + 7^2 + 9^2 = 165.
		

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 (25, -230, 950, -1689, 945).

Crossrefs

Cf. A034472, A074507, A134006.

Programs

Magma

[1^n + 3^n + 5^n + 7^n + 9^n: n in [0..20]]; // Vincenzo Librandi, Jun 20 2011

Mathematica

Table[1^n+3^n+5^n+7^n+9^n,{n,0,30}]

Formula

a(n) = 24*a(n-1) - 206*a(n-2) + 744*a(n-3) - 945*a(n-4) + 384.

G.f.: -(5 - 100*x + 690*x^2 - 1900*x^3 + 1689*x^4)/((-1+x)*(3*x-1)*(9*x-1)*(7*x-1)*(5*x-1)). - R. J. Mathar, Nov 14 2007

a(n) = A134006(n) + A001019(n). - Michel Marcus, Nov 07 2013