A134008 a(n) = 1^n + 3^n + 5^n + 7^n + 9^n + 11^n.

6, 36, 286, 2556, 24310, 240276, 2437006, 25173996, 263567590, 2787694596, 29716508926, 318719062236, 3434943872470, 37162689280116, 403310957409646, 4387917394947276, 47836135613930950, 522357603781540836

Offset: 0

Author

Artur Jasinski, Oct 01 2007

Keywords

• nonn

Examples

			a(3)=286 because 1^2 + 3^2 + 5^2 + 7^2 + 9^2 + 11^2 = 286.
		

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 (36,-505,3480,-12139,19524,-10395).

Crossrefs

Cf. A034472, A074507, A134006, A134007.

Programs

Magma

[1^n + 3^n + 5^n + 7^n + 9^n + 11^n: n in [0..20]]; // Vincenzo Librandi, Jun 20 2011

Mathematica

Table[1^n+3^n+5^n+7^n+9^n+11^n,{n,0,30}]
Join[{6},Table[Total[Range[1,11,2]^n],{n,20}]] (* or *) LinearRecurrence[ {36,-505,3480,-12139,19524,-10395},{6,36,286,2556,24310,240276},20] (* Harvey P. Dale, Apr 20 2015 *)

Formula

a(n) = 35*a(n-1) - 470*a(n-2) + 3010*a(n-3) - 9129*a(n-4) + 10395*a(n-5) - 3840.

G.f.: -2*(6*x-1)*(1627*x^4 - 1752*x^3 + 578*x^2 - 72*x + 3)/((-1+x)*(9*x-1)*(7*x-1)*(3*x-1)*(5*x-1)*(11*x-1)). - R. J. Mathar, Nov 14 2007

a(n) = 36*a(n-1) - 505*a(n-2) + 3480*a(n-3) - 12139*a(n-4) + 19524*a(n-5) - 10395*a(n-6); a(0)=6, a(1)=36, a(2)=286, a(3)=2556, a(4)=24310, a(5)=240276. - Harvey P. Dale, Apr 20 2015