A130845 a(4n) = a(4n+1) = a(4n+2) = A001477(n), a(4n+3) = A005408(n).

0, 0, 0, 1, 1, 1, 1, 3, 2, 2, 2, 5, 3, 3, 3, 7, 4, 4, 4, 9, 5, 5, 5, 11, 6, 6, 6, 13, 7, 7, 7, 15, 8, 8, 8, 17, 9, 9, 9, 19, 10, 10, 10, 21, 11, 11, 11, 23, 12, 12, 12, 25, 13, 13, 13, 27, 14, 14, 14, 29, 15, 15, 15, 31, 16, 16, 16, 33, 17, 17, 17

Offset: 0

Author

Paul Curtz, Jul 20 2007

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).

Programs

Mathematica

CoefficientList[Series[x^3(1+x+x^2+x^3+x^4)/((1-x)^2(1+x)^2(1+x^2)^2),{x,0,80}],x] (* or *) LinearRecurrence[{0,0,0,2,0,0,0,-1},{0,0,0,1,1,1,1,3},80] (* Harvey P. Dale, Mar 04 2012 *)

Formula

O.g.f.: x^3*(1+x+x^2+x^3+x^4)/((1-x)^2*(1+x)^2*(1+x^2)^2). - R. J. Mathar, Aug 22 2008

a(0)=0, a(1)=0, a(2)=0, a(3)=1, a(4)=1, a(5)=1, a(6)=1, a(7)=3, a(n)=2*a(n-4)- a(n-8). - Harvey P. Dale, Mar 04 2012

a(n) = cos(n*Pi/2)/4-(n-1)*(2*sin(n*Pi/2)+(-1)^n-5)/16. - Wesley Ivan Hurt, May 05 2021

Extensions

Edited by N. J. A. Sloane, Sep 28 2007