A391830 a(n) = (1/4) * Sum_{k=0..floor(n/2)} (k+2) * binomial(2*k+2,2*n-4*k+1).

1, 0, 3, 3, 6, 20, 16, 70, 85, 190, 399, 565, 1429, 2114, 4425, 8145, 13877, 28508, 47243, 92523, 165512, 297396, 562390, 982140, 1843714, 3292870, 5975118, 10938740, 19496065, 35751958, 63998039, 115872153, 209435204, 375551494, 680257528, 1218976282, 2197638995, 3950332890

Offset

0,3

Links

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

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

Formula

G.f.: (1-x^2-x^3) / ((1-x^2-x^3)^2 - 4*x^5)^2.

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

Mathematica

CoefficientList[Series[(1-x^2-x^3)/((1-x^2-x^3)^2-4*x^5)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 03 2026 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec((1-x^2-x^3)/((1-x^2-x^3)^2-4*x^5)^2)
(Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! (1-x^2-x^3) / ((1-x^2-x^3)^2 - 4*x^5)^2); // Vincenzo Librandi, Jan 03 2026

Crossrefs

Cf. A391833, A391836.

Sequence in context: A052560 A147836 A384112 * A284710 A377146 A019235

Adjacent sequences: A391827 A391828 A391829 * A391831 A391832 A391833

Keyword

nonn

Author

Seiichi Manyama, Dec 21 2025

Status

approved