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A131174
a(2n) = 2*A000217(n), a(2n+1) = A000217(n).
1
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
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 *)
CROSSREFS
Partial sums of A131119.
Sequence in context: A050137 A086111 A262603 * A291539 A135994 A217646
KEYWORD
nonn
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