A392352 a(n) = Sum_{k=0..floor(3*n/17)} binomial(3*n-16*k,k).

1, 1, 1, 1, 1, 1, 3, 6, 9, 12, 15, 18, 27, 45, 72, 108, 153, 208, 290, 426, 643, 968, 1428, 2055, 2931, 4218, 6159, 9078, 13380, 19572, 28410, 41136, 59721, 87108, 127456, 186462, 272118, 396169, 576300, 839052, 1223475, 1785792, 2606364, 3801030, 5539008, 8069544

Offset

0,7

Links

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

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

Formula

G.f.: (1 - x^6) / (1 - x - 3*x^6 - x^17).

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) + a(n-6) - a(n-7) + a(n-8) - a(n-9) + a(n-10) - a(n-11) + a(n-12) - a(n-13) + a(n-14) - a(n-15) + a(n-16).

Mathematica

CoefficientList[Series[(1-x^6)/(1-x-3*x^6-x^17), {x, 0, 60}], x] (* Vincenzo Librandi, Jan 09 2026 *)

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec((1-x^6)/(1-x-3*x^6-x^17))
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! (1 - x^6) / (1 - x - 3*x^6 - x^17)); // Vincenzo Librandi, Jan 09 2026

Crossrefs

Cf. A001018, A033887, A052544, A099234, A190525, A373638, A373718, A392349, A373640, A392350, A392351.

Sequence in context: A039004 A070021 A083354 * A156242 A384590 A060293

Adjacent sequences: A392349 A392350 A392351 * A392353 A392354 A392355

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 07 2026

Status

approved