A390688 a(n) = Sum_{k=0..floor(2*n/9)} binomial(k+1,2*n-9*k).

1, 0, 0, 0, 0, 2, 0, 0, 0, 1, 3, 0, 0, 0, 4, 4, 0, 0, 1, 10, 5, 0, 0, 6, 20, 6, 0, 1, 21, 35, 7, 0, 8, 56, 56, 8, 1, 36, 126, 84, 9, 10, 120, 252, 120, 11, 55, 330, 462, 165, 23, 220, 792, 792, 221, 90, 715, 1716, 1287, 300, 377, 2002, 3432, 2003, 469, 1379, 5005, 6435

Offset

0,6

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: 1 / ((1-x^5)^2 - x^9).

a(n) = 2*a(n-5) + a(n-9) - a(n-10).

Prog

(PARI) my(N=70, x='x+O('x^N)); Vec(1/((1-x^5)^2-x^9))

Crossrefs

Cf. A001906, A005251, A122514, A392250, A390020, A391399, A390662.

Sequence in context: A244233 A227345 A123262 * A191906 A371647 A187080

Adjacent sequences: A390685 A390686 A390687 * A390689 A390690 A390691

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 12 2026

Status

approved