A213688 a(n) = Sum_{i=0..n} A000129(i)^3.

0, 1, 9, 134, 1862, 26251, 369251, 5196060, 73113372, 1028784997, 14476099149, 203694183170, 2866194639170, 40330419190351, 567492063162119, 7985219303802744, 112360562315573112, 1581033091723823881, 22246823846444284881, 313036566941955454910

Offset: 0

Author

N. J. A. Sloane, Jun 18 2012

Keywords

• nonn
• easy

Links

• Bruno Berselli, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (13,18,-42,11,1).

Crossrefs

Cf. A000129, A048739 (partial sums of A000129), A084158 (sum of squares of A000129).

Cf. A110272 (cubes of the Pell numbers).

Programs

Magma

A110272:=func; [&+[A110272(i): i in [0..n]]: n in [0..19]]; // Bruno Berselli, Jun 21 2012

Mathematica

LinearRecurrence[{13, 18, -42, 11, 1}, {0, 1, 9, 134, 1862}, 20] (* Bruno Berselli, Jun 21 2012 *)

Formula

G.f.: x*(1-4*x-x^2)/((1-x)*(1+2*x-x^2)*(1-14*x-x^2)). [Bruno Berselli, Jun 18 2012]

a(n) = ((3+sqrt(2))*(1+sqrt(2))^(3n+1)+(3-sqrt(2))*(1-sqrt(2))^(3n+1)-21*(-1)^n*((1+sqrt(2))^n+(1-sqrt(2))^n)+32)/224. [Bruno Berselli, Jun 18 2012]