login
A365083
G.f. satisfies A(x) = 1 + x*A(x) / (1 + x)^4.
2
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
0,3
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).
MATHEMATICA
LinearRecurrence[{-3, -6, -4, -1}, {1, 1, -3, 3, 5}, 1 + 33] (* Robert P. P. McKone, Aug 21 2023 *)
PROG
(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n+3*k-1, n-k));
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Seiichi Manyama, Aug 21 2023
STATUS
approved