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

0,3

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).

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.

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 *)

Crossrefs

Sequence in context: A300121 A267046 A308902 * A339560 A360142 A308952

Adjacent sequences: A166512 A166513 A166514 * A166516 A166517 A166518

Keyword

easy,nonn

Author

Paul Barry, Oct 16 2009

Status

approved