A365083 G.f. satisfies A(x) = 1 + x*A(x) / (1 + x)^4.

1, 1, -3, 3, 5, -22, 27, 28, -163, 235, 134, -1188, 1983, 408, -8504, 16320, -1551, -59659, 131507, -46683, -408806, 1040147, -612380, -2721835, 8088003, -6523626, -17457420, 61883839, -62900496, -106248240, 466069760, -571001695, -595520019, 3454539427

Offset: 0

Author

Seiichi Manyama, Aug 21 2023

Keywords

• sign
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (-3,-6,-4,-1).

Crossrefs

Cf. A106510, A127896, A365084.

Cf. A055991.

Programs

Mathematica

LinearRecurrence[{-3, -6, -4, -1}, {1, 1, -3, 3, 5}, 1 + 33] (* Robert P. P. McKone, Aug 21 2023 *)

PARI

a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n+3*k-1, n-k));

Formula

G.f.: A(x) = 1/( 1 - x/(1+x)^4 ).

a(n) = -3*a(n-1) - 6*a(n-2) - 4*a(n-3) - a(n-4) for n > 4.

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n+3*k-1,n-k).