A391399 a(n) = Sum_{k=0..floor(n/3)} binomial(k,2*n-6*k).

1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 3, 0, 1, 6, 1, 1, 10, 5, 1, 15, 15, 2, 21, 35, 8, 28, 70, 29, 37, 126, 85, 54, 210, 211, 100, 331, 463, 231, 506, 925, 573, 781, 1718, 1378, 1287, 3017, 3108, 2366, 5097, 6556, 4823, 8464, 13021, 10388, 14197, 24583, 22509, 24753, 44609

Offset

0,11

Links

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

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

Formula

G.f.: (1-x^3) / ((1-x^3)^2 - x^7).

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

Prog

(PARI) my(A=1, B=1, C=A^2*B, N=1, M=60, x='x+O('x^M), X=1-A*x^3, Y=7); Vec(sum(k=0, N\2, C^k*binomial(N, 2*k)*X^(N-2*k)*x^(Y*k))/(X^2-C*x^Y)^N)

Crossrefs

Cf. A005251, A062200, A391265, A392250.

Sequence in context: A247255 A105147 A335262 * A379625 A111924 A212880

Adjacent sequences: A391396 A391397 A391398 * A391400 A391401 A391402

Keyword

nonn

Author

Seiichi Manyama, Jan 05 2026

Status

approved