A139376 Expansion of 1/((1-x^2*c(x))(1-x-x^2)) where c(x) is the g.f. of A000108.

1, 1, 3, 5, 11, 23, 54, 136, 374, 1103, 3441, 11186, 37472, 128325, 446834, 1576251, 5618950, 20204874, 73190075, 266810125, 978044403, 3602795670, 13329486459, 49509151332, 184540129492, 690061739789, 2587941606367, 9731587992993

Offset

0,3

Comments

Diagonal sums of the Fibonacci-Catalan triangle A139375.

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Formula

a(n) = Sum_{k=0..n} F(k+1)*A132364(n-k).

Conjecture: (-n+1)*a(n) +6*(n-2)*a(n-1) +4*(-2*n+5)*a(n-2) +2*(-n+1)*a(n-3) +3*(3*n-7)*a(n-4) +3*(-n+3)*a(n-5) +2*(-2*n+5)*a(n-6)=0. - R. J. Mathar, Feb 05 2015

Mathematica

g[0]:= 1; g[n_]:= Sum[(i/(n - i))*Binomial[2*n - 3*i - 1, n - 2*i], {i, 0, Floor[n/2]}]; a[n_] := Sum[Fibonacci[k + 1]*g[n - k], {k, 0, n}]; Table[a[n], {n, 0, 25}] (* G. C. Greubel, Oct 20 2016 *)

Crossrefs

Sequence in context: A269964 A305412 A094810 * A074892 A074874 A051439

Adjacent sequences: A139373 A139374 A139375 * A139377 A139378 A139379

Keyword

easy,nonn

Author

Paul Barry, Apr 15 2008

Status

approved