[seqfan] generating functions for toothpick sequences

N. J. A. Sloane njas at research.att.com
Wed May 20 23:43:57 CEST 2009

Dave, using your recurrence for A139251 as a hint,
and using A151550, A151551, A151552, ... as intermediate steps,
I found nice g.f.'s for all the toothpick sequences.

For example, that for A139251 is 

x + 2*x^2 + 4*x^2*(1+x)*(Prod(1+x^(2^k-1)+2*x^(2^k),k=1..oo)-1)/(1+2*x).

New version of OEIS in a few minutes.


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