A038736 a(n) = T(3*n + 1, n + 1), array T as in A038792.

1, 4, 23, 141, 888, 5676, 36622, 237821, 1551727, 10161409, 66732392, 439267525, 2897064773, 19137833146, 126599140313, 838477244705, 5559158604616, 36891869005316, 245025744759152, 1628602268643928, 10832010390274304, 72088640151558145, 480026332241373281, 3198037386794785777, 21315944308822771118

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

G.f.: (g-1)^2/((1-3*g)*(g^2-3*g+1)) where g*(1-g)^2 = x. - Mark van Hoeij, Nov 10 2011

a(n) = A134511(4n,2n). - Alois P. Heinz, Mar 02 2018

a(n) = Sum_{j=0..n} binomial(4*n-j, j). - Petros Hadjicostas, Sep 04 2019

a(n) = hypergeom([1/2 - 2*n, -2*n], [-4*n], -4) - binomial(3*n - 1, n + 1)* hypergeom([1, 1 - n, 3/2 - n], [1 - 3*n, n + 2], -4) for n > 0. - Peter Luschny, Sep 04 2019

a(n) ~ 3^(3*n + 1/2) / (sqrt(Pi*n) * 2^(2*n-1)). - Vaclav Kotesovec, Sep 04 2019

From Seiichi Manyama, Nov 01 2025: (Start)

G.f.: 1/((1-3*x*g^2) * (1-x*g^4)) where g = 1+x*g^3 is the g.f. of A001764.

a(n) = Sum_{k=0..n} binomial(3*n,n-k) * Fibonacci(k+1). (End)

Maple

a := n -> `if`(n=0, 1, hypergeom([1/2 - 2*n, -2*n], [-4*n], -4) - binomial(3*n - 1, n + 1)*hypergeom([1, 1 - n, 3/2 - n], [1 - 3*n, n + 2], -4)):
seq(simplify(a(n)), n = 0..24); # Peter Luschny, Sep 04 2019

Crossrefs

Cf. A108080, A122367.

Cf. A038744, A390238.

Cf. A000045, A001764, A038792, A134511.

Sequence in context: A290052 A158197 A356282 * A091642 A162561 A277921

Adjacent sequences: A038733 A038734 A038735 * A038737 A038738 A038739

Keyword

nonn

Author

Clark Kimberling, May 02 2000

Status

approved