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

0,3

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).

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

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 *)

Prog

(PARI) a(n)=my(q=n\2); q*[2*q+2, q+1][n%2+1]/2 \\ Charles R Greathouse IV, Jun 03 2026

Crossrefs

Partial sums of A131119.

Cf. A000217.

Sequence in context: A050137 A086111 A262603 * A291539 A135994 A217646

Adjacent sequences: A131171 A131172 A131173 * A131175 A131176 A131177

Keyword

nonn,easy,changed

Author

Paul Curtz, Sep 24 2007

Extensions

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

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

Status

approved