A229393 Number of shapes of balanced 8-ary trees with n nodes, where a tree is balanced if the total number of nodes in subtrees corresponding to the branches of any node differ by at most one.

1, 1, 8, 28, 56, 70, 56, 28, 8, 1, 64, 1792, 28672, 286720, 1835008, 7340032, 16777216, 16777216, 469762048, 5754585088, 40282095616, 176234168320, 493455671296, 863547424768, 863547424768, 377801998336, 6044831973376, 42313823813632, 169255295254528

Offset: 0

Author

Alois P. Heinz, Sep 21 2013

Keywords

• nonn

Comments

a(n) = 1 for n in { A023001 }.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..585

Crossrefs

Column k=8 of A221857.

Programs

Maple

a:= proc(n) option remember; local m, r; if n<2 then 1 else
      r:= iquo(n-1, 8, 'm'); binomial(8, m) *a(r+1)^m *a(r)^(8-m) fi
    end:
seq(a(n), n=0..73);