|
%I #21 Feb 24 2023 16:34:24
%S 0,1,1,1,2,2,4,5,9,15,28,45,73,116,199,345,601,1021,1738,2987,5244,
%T 9321,16720,30103,54345,97996,176011,314045,556577,980852,1722451,
%U 3020214,5298570,9316456,16440262,29136489,51860214,92643425,165934156
%N Number of B-trees of order 4 with n leaves.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/B-Tree.html">B-tree</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F G.f. A(x) satisfies: A(x) = x + A(x^2+x^3+x^4). [_Geoffrey Critzer_, Mar 28 2013]
%p spec := [ B, {B=Union(Z, Subst(M, B)), M=Union(Prod(Z,Z),Prod(Z,Z,Z),Prod(Z$4))} ]: [ seq(combstruct[count](spec, size=n), n=0..42) ];
%t nn=38;f[x_]:=Sum[a[n]x^n,{n,0,nn}];a[0]=0;sol=SolveAlways[0==Series[f[x]-x-f[x^2+x^3+x^4],{x,0,nn}],x];Table[a[n],{n,0,nn}]/.sol (* _Geoffrey Critzer_, Mar 28 2013 *)
%Y Cf. A014535.
%K nonn
%O 0,5
%A _N. J. A. Sloane_, _Paul Zimmermann_
|
