A392490 a(n) = Sum_{k=0..floor(n/3)} binomial(k+1,2*n-6*k+1).

1, 0, 0, 2, 0, 0, 3, 1, 0, 4, 4, 0, 5, 10, 1, 6, 20, 6, 7, 35, 21, 9, 56, 56, 17, 84, 126, 46, 121, 252, 131, 175, 462, 342, 275, 793, 805, 506, 1299, 1730, 1079, 2080, 3448, 2457, 3367, 6465, 5565, 5733, 11562, 12121, 10556, 20026, 25142, 20944, 34223, 49725

Offset

0,4

Links

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

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

Formula

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

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

Prog

(PARI) my(N=60, x='x+O('x^N)); Vec(1/((1-x^3)^2-x^7))

Crossrefs

Cf. A005314, A392489, A392491.

Cf. A390020, A390662.

Sequence in context: A029301 A263414 A162934 * A303908 A351592 A082660

Adjacent sequences: A392487 A392488 A392489 * A392491 A392492 A392493

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 14 2026

Status

approved