A392675 a(n) = Sum_{k=0..floor(n/3)} binomial(k+1,3*n-9*k+1).

1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 1, 0, 5, 5, 0, 6, 15, 0, 7, 35, 1, 8, 70, 8, 9, 126, 36, 10, 210, 120, 12, 330, 330, 23, 495, 792, 79, 715, 1716, 300, 1002, 3432, 1016, 1379, 6435, 3019, 1925, 11440, 8025, 2940, 19449, 19466, 5440, 31841, 43777, 12444, 50541, 92398, 31977, 78489

Offset

0,4

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1,1).

Formula

G.f.: (1-x^3) / ((1-x^3)^3 - x^10).

a(n) = 3*a(n-3) - 3*a(n-6) + a(n-9) + a(n-10).

Prog

(PARI) my(N=60, x='x+O('x^N)); Vec((1-x^3)/((1-x^3)^3-x^10))

Crossrefs

Cf. A390037, A392273.

Sequence in context: A280728 A175676 A384627 * A390158 A035377 A136274

Adjacent sequences: A392672 A392673 A392674 * A392676 A392677 A392678

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 19 2026

Status

approved