A392349 a(n) = Sum_{k=0..floor(3*n/8)} binomial(3*n-7*k,k).

1, 1, 1, 3, 6, 9, 18, 36, 64, 119, 228, 423, 786, 1479, 2766, 5160, 9661, 18078, 33786, 63192, 118212, 221049, 413391, 773187, 1445995, 2704246, 5057593, 9458770, 17689720, 33083548, 61873249, 115715596, 216412235, 404736228, 756940609, 1415636084, 2647534488

Offset

0,4

Links

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

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

Formula

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

a(n) = a(n-1) + 3*a(n-3) + a(n-8).

Mathematica

CoefficientList[Series[(1-x^3)/(1-x-3*x^3-x^8), {x, 0, 60}], x] (* Vincenzo Librandi, Jan 09 2026 *)
LinearRecurrence[{1, 0, 3, 0, 0, 0, 0, 1}, {1, 1, 1, 3, 6, 9, 18, 36}, 40] (* Harvey P. Dale, Jan 11 2026 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec((1-x^3)/(1-x-3*x^3-x^8))
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! (1 - x^3) / (1 - x - 3*x^3 - x^8)); // Vincenzo Librandi, Jan 09 2026

Crossrefs

Cf. A001018, A033887, A052544, A099234, A190525, A373638, A373718, A373640, A392350, A392351, A392352.

Sequence in context: A182751 A057576 A100852 * A342596 A363124 A018186

Adjacent sequences: A392346 A392347 A392348 * A392350 A392351 A392352

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 07 2026

Status

approved