A107068 Expansion of 1/((1+x)^3-x^4).

1, -3, 6, -10, 16, -27, 49, -92, 172, -316, 573, -1035, 1874, -3406, 6204, -11303, 20577, -37432, 68072, -123800, 225193, -409683, 745342, -1355970, 2466760, -4487395, 8163217, -14850196, 27015092, -49145300, 89404037, -162641499, 295872778, -538243174, 979156724, -1781254927, 3240410561

Offset

0,2

Links

Table of n, a(n) for n=0..36.

Index entries for linear recurrences with constant coefficients, signature (-3,-3,-1,1).

Formula

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

a(n) = Sum_{k=0..n+4} (-1)^(n-k)*C(n+4, k) * Sum_{j=0..floor(k/4)} C(k-3*j, j).

a(n) = (-1)^n * Sum_{k=0..floor(n/4)} binomial(n-k+2,n-4*k). - Seiichi Manyama, Jan 15 2026

Mathematica

LinearRecurrence[{-3, -3, -1, 1}, {1, -3, 6, -10}, 40] (* Harvey P. Dale, Jul 16 2018 *)

Crossrefs

Cf. A077990.

Sequence in context: A265074 A054886 A130578 * A033541 A038505 A369850

Adjacent sequences: A107065 A107066 A107067 * A107069 A107070 A107071

Keyword

easy,sign

Author

Paul Barry, May 10 2005

Status

approved