A117572 Expansion of (1 + 2*x^2)/((1 - x^2)*(1 - x^3)).

1, 0, 3, 1, 3, 3, 4, 3, 6, 4, 6, 6, 7, 6, 9, 7, 9, 9, 10, 9, 12, 10, 12, 12, 13, 12, 15, 13, 15, 15, 16, 15, 18, 16, 18, 18, 19, 18, 21, 19, 21, 21, 22, 21, 24, 22, 24, 24, 25, 24, 27, 25, 27, 27, 28, 27, 30, 28, 30, 30, 31, 30, 33, 31, 33, 33, 34, 33, 36, 34, 36, 36, 37, 36, 39, 37

Offset: 0

Author

Paul Barry, Mar 29 2006

Keywords

• easy
• nonn

Comments

Diagonal sums of A110128 [this cross-reference is wrong - N. J. A. Sloane, Jan 01 2008]. Partial sums are A117573.

Links

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

Programs

Maxima

a(n):=(n+1)/2+3/4*(-1)^n+1/12-(1/3)*(-2)^fix(mod(n,3)/2); /* Tani Akinari, Nov 10 2012 */

Formula

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

a(n) = cos(2*Pi*n/3+Pi/3)/3-sin(2*Pi*n/3+Pi/3)/sqrt(3)+3(-1)^n/4+(6n+7)/12.

a(n) = Sum_{k=0..floor(n/2)} 2*A001045(L((n-2k+2)/3)) where L(j/p) is the Legendre symbol of j and p.