A185648 Expansion of g.f. 1/ (1-x^1*(1-x^(m+1))/ (1-x^2*(1-x^(m+2))/ (1- ... ))) for m=8.

1, 1, 1, 2, 3, 5, 9, 15, 26, 45, 77, 133, 230, 397, 687, 1188, 2054, 3553, 6145, 10629, 18385, 31802, 55010, 95156, 164600, 284725, 492519, 851962, 1473732, 2549275, 4409764, 7628058, 13195104, 22825046, 39483039, 68298240, 118143130, 204365438, 353513851

Offset: 0

Author

Alois P. Heinz, Aug 29 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..750
• Paul D. Hanna et al., Formula Needed for a Family of Continued Fractions and follow-up messages on the SeqFan list, Jul 28 2013

Crossrefs

Column m=8 of A185646.

Programs

Mathematica

nMax = 39; col[m_ /; 0 <= m <= nMax] := 1/(1 + ContinuedFractionK[-x^k (1 - x^(m + k)), 1, {k, 1, Ceiling[nMax/2]}]) + O[x]^(2 nMax) // CoefficientList[#, x]&; A185648 = col[8][[1 ;; nMax]] (* Jean-François Alcover, Nov 03 2016 *)

Formula

a(n) ~ c * d^n, where d = 1.729812413755051803149808764090629506945619020643782294236248965..., c = 0.319480257502538464183377228844611044469159258446802374119607096... . - Vaclav Kotesovec, Sep 04 2014