A361727 Diagonal of rational function 1/(1 - (1 + x*y) * (x^3 + y^3)).

1, 0, 0, 2, 4, 2, 6, 24, 36, 44, 126, 300, 470, 860, 2080, 4192, 7420, 15260, 33124, 64568, 124558, 259632, 535668, 1055460, 2118414, 4373412, 8872644, 17765396, 36138168, 73972404, 149793424, 303140552, 618565948, 1261454064, 2561056212, 5211145368

Offset

0,4

Links

Winston de Greef, Table of n, a(n) for n = 0..3162

Formula

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

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

From Vaclav Kotesovec, Mar 22 2023: (Start)

Recurrence: n*a(n) = 2*(2*n-3)*a(n-3) + 8*(n-2)*a(n-4) + 2*(2*n-5)*a(n-5).

a(n) ~ 1 / (sqrt((5 - 8*r^3 - 8*r^4)*Pi*n) * r^n), where r = 0.484163615233802299545617907511361266999078019358842974840776720... is the real root of the equation -1 + 4*r^3 + 8*r^4 + 4*r^5 = 0. (End)

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(2*k, k)*binomial(2*k, n-3*k));

Crossrefs

Cf. A137635, A361726.

Sequence in context: A021012 A229460 A154120 * A261964 A177847 A296471

Adjacent sequences: A361724 A361725 A361726 * A361728 A361729 A361730

Keyword

nonn

Author

Seiichi Manyama, Mar 22 2023

Status

approved