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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 (list; graph; refs; listen; history; text; internal format)
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)^(6-m), where n >= 0 and 0 <= m <= 6.

MAPLE

a:= proc(n) option remember; local m, r; if n<2 then 1 else

      r:= iquo(n-1, 6, 'm'); binomial(6, m) *a(r+1)^m *a(r)^(6-m) fi

    end:

seq(a(n), n=0..50);  # Alois P. Heinz, Apr 10 2013

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

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Last modified February 24 21:22 EST 2018. Contains 299628 sequences. (Running on oeis4.)