A131174 a(2n) = 2*A000217(n), a(2n+1) = A000217(n).

0, 0, 2, 1, 6, 3, 12, 6, 20, 10, 30, 15, 42, 21, 56, 28, 72, 36, 90, 45, 110, 55, 132, 66, 156, 78, 182, 91, 210, 105, 240, 120, 272, 136, 306, 153, 342, 171, 380, 190, 420, 210, 462, 231, 506, 253, 552, 276, 600, 300, 650, 325, 702, 351, 756, 378, 812, 406, 870, 435

Offset: 0

Author

Paul Curtz, Sep 24 2007

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0, 3, 0, -3, 0, 1).

Crossrefs

Partial sums of A131119.

Programs

Maple

A000217 := proc(n) n*(n+1)/2 ; end: A131174 := proc(n) if n mod 2 = 0 then 2*A000217(n/2) ; else A000217((n-1)/2) ; fi ; end: seq(A131174(n),n=0..90) ; # R. J. Mathar, Oct 26 2007

Mathematica

LinearRecurrence[{0,3,0,-3,0,1},{0,0,2,1,6,3},60] (* Harvey P. Dale, Jun 01 2012 *)

Formula

a(n) = 3*a(n-2)-3*a(n-4)+a(n-6).

G.f.: x^2*(2+x)/((1-x)^3*(1+x)^3). [R. J. Mathar, Jul 17 2009]

a(n) = (3*n^2+4*n-1+(n^2+4*n+1)*(-1)^n)/16. - Luce ETIENNE, Aug 19 2014

Extensions

Edited by N. J. A. Sloane, Sep 27 2007

More terms from R. J. Mathar, Oct 26 2007