A392272 a(n) = Sum_{k=0..floor(3*n/8)} binomial(k,3*n-8*k).

1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 4, 1, 0, 10, 1, 1, 20, 1, 7, 35, 1, 28, 56, 2, 84, 84, 11, 210, 120, 56, 462, 166, 221, 924, 233, 716, 1716, 377, 2003, 3004, 819, 5006, 5021, 2275, 11441, 8144, 6748, 24312, 13192, 19244, 48640, 22440, 51204, 92569, 42636

Offset

0,12

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,-3,0,1,1).

Formula

G.f.: (1-x^3)^2 / ((1-x^3)^3 - x^8).

a(n) = 3*a(n-3) - 3*a(n-6) + a(n-8) + a(n-9).

Mathematica

CoefficientList[Series[(1-x^3)^2/((1-x^3)^3-x^8), {x, 0, 60}], x] (* Vincenzo Librandi, Jan 07 2026 *)

Prog

(PARI) my(N=60, x='x+O('x^N)); Vec((1-x^3)^2/((1-x^3)^3-x^8))
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1-x^3)^2 / ((1-x^3)^3 - x^8)); // Vincenzo Librandi, Jan 07 2026

Crossrefs

Cf. A003522, A392253, A392271, A392273.

Cf. A373640.

Sequence in context: A089962 A394437 A363971 * A127155 A211793 A145880

Adjacent sequences: A392269 A392270 A392271 * A392273 A392274 A392275

Keyword

nonn

Author

Seiichi Manyama, Jan 05 2026

Status

approved