A389718 a(n) = Sum_{k=0..floor(5*n/14)} binomial(k,5*n-14*k).

1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 6, 1, 0, 21, 1, 0, 56, 1, 0, 126, 1, 1, 252, 1, 11, 462, 1, 66, 792, 1, 286, 1287, 1, 1001, 2002, 2, 3003, 3003, 17, 8008, 4368, 137, 19448, 6188, 817, 43758, 8568, 3877, 92378, 11629, 15505, 184756, 15525, 54265, 352716, 20580

Offset

0,18

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,5,0,0,-10,0,0,10,0,0,-5,0,1,1).

Formula

G.f.: (1-x^3)^4 / ((1-x^3)^5 - x^14).

a(n) = 5*a(n-3) - 10*a(n-6) + 10*a(n-9) - 5*a(n-12) + a(n-14) + a(n-15).

Prog

(PARI) my(N=70, x='x+O('x^N)); Vec((1-x^3)^4/((1-x^3)^5-x^14))

Crossrefs

Cf. A099131, A099132, A392356.

Cf. A389717, A391265, A392272.

Sequence in context: A127573 A351110 A137388 * A302971 A114153 A119832

Adjacent sequences: A389715 A389716 A389717 * A389719 A389720 A389721

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 08 2026

Status

approved