A166515 Partial sum of A166514.

0, 1, 2, 2, 4, 5, 8, 8, 12, 13, 18, 18, 24, 25, 32, 32, 40, 41, 50, 50, 60, 61, 72, 72, 84, 85, 98, 98, 112, 113, 128, 128, 144, 145, 162, 162, 180, 181, 200, 200, 220, 221, 242, 242, 264, 265, 288, 288, 312, 313, 338, 338, 364, 365, 392, 392, 420, 421, 450, 450, 480

Offset: 0

Author

Paul Barry, Oct 16 2009

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,-1,-1,1).

Programs

Mathematica

CoefficientList[Series[x (1 + x - x^2 + x^3)/((1 + x)^2*(1 - x)^3*(1 + x^2)), {x, 0, 50}], x] (* G. C. Greubel, May 15 2016 *)
LinearRecurrence[{1,1,-1,1,-1,-1,1},{0,1,2,2,4,5,8},70] (* Harvey P. Dale, Jan 16 2017 *)

Formula

G.f.: x(1+x-x^2+x^3)/((1+x)^2*(1-x)^3*(1+x^2)).

a(n) = (2n^2+6n+5)/16 + (2n-1)*(-1)^n/16 - sqrt(2)*cos(Pi*n/2+Pi/4)/4.