A077905 Expansion of 1/(1 - x^2 - x^3 + x^4).

1, 0, 1, 1, 0, 2, 0, 1, 2, -1, 3, 0, 0, 4, -3, 4, 1, -3, 8, -6, 4, 5, -10, 15, -9, 0, 16, -24, 25, -8, -15, 41, -48, 34, 8, -55, 90, -81, 27, 64, -144, 172, -107, -36, 209, -315, 280, -70, -244, 525, -594, 351, 175, -768, 1120, -944, 177, 944, -1887, 2065, -1120, -766, 2832, -3951, 3186, -353, -3597, 6784, -7136

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Examples

			G.f. = 1 + x^2 + x^3 + 2*x^5 + x^7 + 2*x^8 - x^9 + 3*x^10 + 4*x^13 + ...
		

Links

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

Crossrefs

Cf. A023434.

Programs

Mathematica

CoefficientList[ Series[1/((1 - x) (1 + x - x^3)), {x, 0, 68}], x] (* Robert G. Wilson v, Oct 29 2011 *)

Formula

a(n) = sum(k=1..n/2, sum(j=0..k, binomial(j,n-4*k+2*j)*(-1)^(k-j)*binomial(k,j))), n>0, a(0)=1. - Vladimir Kruchinin, Oct 21 2011

a(-3-n) = -A023434(n) for all n in Z. - Michael Somos, Sep 25 2014