%I A063894
%S A063894 2,1,2,4,10,25,68,187,532,1532,4492,13308,39870,120433,366656,1123504,
%T A063894 3463050,10729234,33396202,104381385,327477814,1030903514,3255394686,
%U A063894 10309154738,32732315724,104177891232,332308237666,1062192108053
%N A063894 Start with x, y; then concatenate each word in turn with all preceding 
               words, getting x y xy xxy yxy xxxy yxxy xyxxy ...; sequence gives 
               number of words of length n. Also binary trees by degree: x y (x,
               y) (x,(x,y)) (y,(x,y)) (x,(x,(x,y))) (y,(x,(x,y))) ((x,y),(x,(x,y)))...
%F A063894 G.f. A(x)=1-sqrt(1-4x+A(x^2)) satisfies A(x)^2-2A(x)+4x-A(x^2)=0, A(0)=0. 
               - Michael Somos, Sep 06 2003
%F A063894 a(n)=(sum a(i)a(j), i+j=n, i<j)+(if n=2k, (a(k)-1)a(k)/2), n>1. a(1)=2.
%o A063894 (PARI) a(n)=local(A,m); if(n<0,0,m=1; A=O(x); while(m<=n,m*=2; A=1-sqrt(1-4*x+subst(A,
               x,x^2))); polcoeff(A,n))
%Y A063894 Cf. A063895.
%Y A063894 Sequence in context: A029728 A135547 A146307 this_sequence A024500 A000087 
               A145667
%Y A063894 Adjacent sequences: A063891 A063892 A063893 this_sequence A063895 A063896 
               A063897
%K A063894 easy,nonn,nice
%O A063894 1,1
%A A063894 Claude Lenormand (claude.lenormand(AT)free.fr), Aug 29 2001