A037026 Number of B-trees of order 4 with n leaves.

0, 1, 1, 1, 2, 2, 4, 5, 9, 15, 28, 45, 73, 116, 199, 345, 601, 1021, 1738, 2987, 5244, 9321, 16720, 30103, 54345, 97996, 176011, 314045, 556577, 980852, 1722451, 3020214, 5298570, 9316456, 16440262, 29136489, 51860214, 92643425, 165934156

Offset: 0

Author

N. J. A. Sloane, Paul Zimmermann

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, B-tree
• Index entries for sequences related to rooted trees

Crossrefs

Cf. A014535.

Programs

Maple

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) ];

Mathematica

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 *)

Formula

G.f. A(x) satisfies: A(x) = x + A(x^2+x^3+x^4). [Geoffrey Critzer, Mar 28 2013]