A238428 - OEIS

%I #8 Aug 22 2014 13:13:29

%S 1,1,1,3,6,17,42,118,321,920,2626,7679,22554,67115,200883,606238,

%T 1839448,5613892,17211963,53006846,163866246,508389780,1582286912,

%U 4939146731,15459006948,48505063741,152539740067,480726546083,1517979996460,4802074019769,15217153748772,48298352064093,153526087484475

%N Expansion of F(x) where F(x) = 1 + x / (1 - x * F(x) - x^2 * F(x^2) ).

%C What does this sequence count?

%H Alois P. Heinz, <a href="/A238428/b238428.txt">Table of n, a(n) for n = 0..500</a>

%F a(n) ~ c * d^n / n^(3/2), where d = 3.3305741143240040687593..., c = 0.544842763137687191994... . - _Vaclav Kotesovec_, Aug 22 2014

%o (PARI)

%o N=66;  R=O('x^N);  x='x+R;

%o F = 1;  for (k=1, N+1, F = 1 + x / (1 - x * F - x^2 * subst(F, 'x, 'x^2) ) + R; );

%o Vec(F)

%K nonn

%O 0,4

%A _Joerg Arndt_, Feb 28 2014