A166593 Partial sums of A166592.

0, 1, 4, 6, 9, 10, 10, 9, 6, 4, 1, 0, 0, 1, 4, 6, 9, 10, 10, 9, 6, 4, 1, 0, 0, 1, 4, 6, 9, 10, 10, 9, 6, 4, 1, 0, 0, 1, 4, 6, 9, 10, 10, 9, 6, 4, 1, 0, 0, 1, 4, 6, 9, 10, 10, 9, 6, 4, 1, 0, 0, 1, 4, 6, 9, 10, 10, 9, 6, 4, 1, 0, 0, 1, 4, 6, 9, 10, 10, 9, 6, 4, 1, 0, 0, 1, 4, 6, 9, 10, 10, 9, 6, 4, 1, 0, 0

Offset

0,3

Links

Table of n, a(n) for n=0..96.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1,-1,1).

Formula

G.f.: x(1+3x+x^2)/((1-x)(1-x^2+x^4)) = x(1+3x+x^2)/(1-x-x^2+x^3+x^4-x^5).

a(n) = a(n-1) + a(n-2) - a(n-3) - a(n-4) + a(n-5).

a(n) = (sqrt(8) - sqrt(6))*cos(5*Pi*n/6 + 5*Pi/12)-(sqrt(8) + sqrt(6))*cos(Pi*n/6 + Pi/12) + 5.

a(n + 12) = a(n). - G. C. Greubel, May 18 2016

Mathematica

LinearRecurrence[{1, 1, -1, -1, 1}, {0, 1, 4, 6, 9}, 25] (* G. C. Greubel, May 18 2016 *)

Crossrefs

Sequence in context: A163297 A051679 A010378 * A196269 A124785 A010404

Adjacent sequences: A166590 A166591 A166592 * A166594 A166595 A166596

Keyword

easy,nonn

Author

Paul Barry, Oct 17 2009

Status

approved