

A131892


a(n) is the number of shapes of balanced trees with constant branching factor 6 and n nodes. The node is balanced if the size, measured in nodes, of each pair of its children differ by at most one node.


6



1, 1, 6, 15, 20, 15, 6, 1, 36, 540, 4320, 19440, 46656, 46656, 699840, 4374000, 14580000, 27337500, 27337500, 11390625, 91125000, 303750000, 540000000, 540000000, 288000000, 64000000, 288000000, 540000000, 540000000, 303750000, 91125000, 11390625, 27337500
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OFFSET

0,3


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..259
Jeffrey A. Barnett, Counting Balanced Tree Shapes.


FORMULA

a(0) = a(1) = 1; a(6n+1+m) = (6 choose m) * a(n+1)^m * a(n)^(6m), where n >= 0 and 0 <= m <= 6.


MAPLE

a:= proc(n) option remember; local m, r; if n<2 then 1 else
r:= iquo(n1, 6, 'm'); binomial(6, m) *a(r+1)^m *a(r)^(6m) fi
end:
seq(a(n), n=0..50); # Alois P. Heinz, Apr 10 2013


MATHEMATICA

a[n_, k_] := a[n, k] = Module[{m, r}, If[n < 2  k == 1, 1, If[k == 0, 0, {r, m} = QuotientRemainder[n  1, k]; Binomial[k, m]*a[r + 1, k]^m*a[r, k]^(k  m)]]];
a[n_] := a[n, 6];
Table[a[n], {n, 0, 50}] (* JeanFrançois Alcover, Jun 04 2018, after Alois P. Heinz *)


CROSSREFS

Cf. A110316, A131889, A131890, A131891, A131893.
Column k=6 of A221857.  Alois P. Heinz, Apr 17 2013
Sequence in context: A176849 A087110 A063266 * A291381 A280719 A282173
Adjacent sequences: A131889 A131890 A131891 * A131893 A131894 A131895


KEYWORD

easy,nonn


AUTHOR

Jeffrey A. Barnett (jbb(AT)notatt.com), Jul 24 2007


STATUS

approved



