A228646 Expansion of g.f. 1/ (1-x^1*(1-x^(m+1))/ (1-x^2*(1-x^(m+2))/ (1- ... ))) for m=6.

1, 1, 1, 2, 3, 5, 9, 15, 25, 43, 74, 126, 217, 372, 638, 1096, 1881, 3230, 5546, 9524, 16353, 28083, 48224, 82811, 142208, 244204, 419360, 720144, 1236670, 2123670, 3646879, 6262611, 10754485, 18468174, 31714525, 54461873, 93524824, 160605817, 275800867

Offset: 0

Author

Alois P. Heinz, Aug 28 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• 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

Cf. A143064 (m=0), A227360 (m=2), A173173 (m=3), A227374 (m=4), A227375 (m=5), A228644 (m=7), A228645 (m=9).

Column m=6 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]&; A228646 = col[6][[1 ;; nMax]] (* Jean-François Alcover, Nov 03 2016 *)