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

0,3

Comments

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

Links

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

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);

Crossrefs

Column k=8 of A221857.

Sequence in context: A009504 A001486 A230211 * A173681 A045850 A264354

Adjacent sequences: A229390 A229391 A229392 * A229394 A229395 A229396

Keyword

nonn

Author

Alois P. Heinz, Sep 21 2013

Status

approved