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A075864 G.f. satisfies A(x) = 1 + Sum_{n>=0} (x*A(x))^(2^n). 1
1, 1, 2, 4, 10, 26, 72, 204, 594, 1762, 5318, 16270, 50360, 157392, 496016, 1574432, 5028962, 16152194, 52133154, 169004450, 550036778, 1796512970, 5886709502, 19346204982, 63751851400, 210605429496, 697337388556, 2313871053172 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Conjecture: Number of Dyck n-paths with all ascent lengths being a power of 2. [David Scambler, May 07 2012]

LINKS

Table of n, a(n) for n=0..27.

MATHEMATICA

seq = {};

f[x_, y_, d_] :=

  f[x, y, d] =

   If[x < 0 || y < x , 0,

    If[x == 0 && y == 0, 1,

     f[x - 1, y, 0] + f[x, y - If[d == 0, 1, d], If[d == 0, 1, 2*d]]]];

For[n = 0, n <= 27, n++, seq = Append[seq, f[n, n, 0]]]; seq

(* David Scambler, May 07 2012 *)

CROSSREFS

Cf. A075853.

Sequence in context: A149813 A149814 A125108 * A180023 A154835 A049145

Adjacent sequences:  A075861 A075862 A075863 * A075865 A075866 A075867

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 15 2002

STATUS

approved

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Last modified November 21 05:01 EST 2017. Contains 294988 sequences.