A376727 Expansion of (1 + x^3 - x^4)/((1 + x^3 - x^4)^2 - 4*x^3).

1, 0, 0, 3, 1, 0, 5, 10, 1, 7, 35, 21, 10, 84, 126, 47, 166, 462, 343, 341, 1288, 1731, 1170, 3081, 6453, 5685, 7553, 19572, 25280, 24004, 52789, 93844, 95932, 143435, 299577, 386536, 448673, 873754, 1411193, 1625003, 2536215, 4639077, 6097214, 7959492, 14238226

Offset

0,4

Links

Table of n, a(n) for n=0..44.

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

Formula

a(n) = 2*a(n-3) + 2*a(n-4) - a(n-6) + 2*a(n-7) - a(n-8).

a(n) = Sum_{k=0..floor(n/3)} binomial(2*k+1,2*n-6*k+1).

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec((1+x^3-x^4)/((1+x^3-x^4)^2-4*x^3))
(PARI) a(n) = sum(k=0, n\3, binomial(2*k+1, 2*n-6*k+1));

Crossrefs

Cf. A099511, A376726, A376728.

Cf. A376724, A376730.

Sequence in context: A175779 A280819 A300280 * A135670 A096754 A021767

Adjacent sequences: A376724 A376725 A376726 * A376728 A376729 A376730

Keyword

nonn

Author

Seiichi Manyama, Oct 03 2024

Status

approved