A112518 Expansion of g.f. 1/(1 - x + 2*x^3 + x^4).

1, 1, 1, -1, -4, -7, -6, 3, 21, 40, 40, -5, -106, -226, -256, -39, 519, 1257, 1591, 592, -2441, -6880, -9655, -5365, 10836, 37026, 57411, 41104, -43784, -195632, -335251, -288787, 146261, 1012395, 1925220, 1921485, -249566, -5112401, -10880591, -12302944

Offset: 0

Author

Paul Barry, Sep 09 2005

Keywords

• easy
• sign

Links

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

Crossrefs

Row sums of A112517.

Programs

Mathematica

LinearRecurrence[{1,0,-2,-1},{1,1,1,-1},40] (* James C. McMahon, Jun 07 2024 *)

Formula

a(n) = a(n-1) - 2*a(n-3) - a(n-4).

a(n) = Sum_{k=0..n} Sum_{j=0..n} C(j, n-j)*C(k, j-k)*(-1)^(j-k).