A391831 a(n) = (1/4) * Sum_{k=0..floor(n/3)} (n-2*k+2) * binomial(2*n-4*k+2,2*k+1).

1, 3, 6, 13, 35, 91, 214, 491, 1151, 2711, 6290, 14427, 33010, 75444, 171786, 389500, 880533, 1986357, 4471290, 10042661, 22511404, 50374282, 112545858, 251073154, 559324988, 1244426930, 2765391188, 6138444816, 13611448023, 30152472569, 66732950720, 147563807981, 326033813397

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (4,-6,8,-5,-4,-2,-4,-6,4,4,0,-1).

Formula

G.f.: (1-x-x^3) / ((1-x-x^3)^2 - 4*x^4)^2.

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

Mathematica

CoefficientList[Series[(1-x-x^3)/((1-x-x^3)^2-4*x^4)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 03 2026 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec((1-x-x^3)/((1-x-x^3)^2-4*x^4)^2)
(Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! (1-x-x^3) / ((1-x-x^3)^2 - 4*x^4)^2); // Vincenzo Librandi, Jan 03 2026

Crossrefs

Cf. A391834, A391837.

Sequence in context: A104448 A352864 A062466 * A366940 A053564 A389250

Adjacent sequences: A391828 A391829 A391830 * A391832 A391833 A391834

Keyword

nonn

Author

Seiichi Manyama, Dec 21 2025

Status

approved