A166515 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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 *)