A391829 a(n) = (1/4) * Sum_{k=0..n} (k+2) * binomial(2*k+2,2*n-2*k+1).

1, 3, 9, 30, 91, 271, 801, 2330, 6710, 19172, 54386, 153362, 430257, 1201685, 3343079, 9268130, 25614741, 70595817, 194078465, 532337092, 1457119612, 3980884648, 10856936212, 29562266740, 80375490401, 218228740855, 591758714965, 1602726816070, 4336011986495

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,-2,0,-11,0,-2,4,-1).

Formula

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

a(n) = 4*a(n-1) - 2*a(n-2) - 11*a(n-4) - 2*a(n-6) + 4*a(n-7) - a(n-8).

Mathematica

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec((1-x-x^2)/((1-x-x^2)^2-4*x^3)^2)
(Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! (1-x-x^2) / ((1-x-x^2)^2 - 4*x^3)^2); // Vincenzo Librandi, Jan 03 2026

Crossrefs

Cf. A391832, A391835.

Cf. A381421.

Sequence in context: A078844 A374626 A144817 * A337267 A337034 A250128

Adjacent sequences: A391826 A391827 A391828 * A391830 A391831 A391832

Keyword

nonn

Author

Seiichi Manyama, Dec 21 2025

Status

approved