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A131891 a(n) is the number of shapes of balanced trees with constant branching factor 5 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, 5, 10, 10, 5, 1, 25, 250, 1250, 3125, 3125, 31250, 125000, 250000, 250000, 100000, 500000, 1000000, 1000000, 500000, 100000, 250000, 250000, 125000, 31250, 3125, 3125, 1250, 250, 25, 1, 125, 6250, 156250, 1953125, 9765625, 488281250, 9765625000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..781

Jeffrey Barnett, Counting Balanced Tree Shapes

FORMULA

a(0) = a(1) = 1; a(5n+1+m) = (5 choose m) * a(n+1)^m * a(n)^(5-m), where n >= 0 and 0 <= m <= 5.

MAPLE

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

      r:= iquo(n-1, 5, 'm'); binomial(5, m) *a(r+1)^m *a(r)^(5-m) 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, 5];

Table[a[n], {n, 0, 50}] (* Jean-Fran├žois Alcover, Jun 04 2018, after Alois P. Heinz *)

CROSSREFS

Cf. A110316, A131889, A131890, A131892, A131893.

Column k=5 of A221857. - Alois P. Heinz, Apr 17 2013

Sequence in context: A277950 A087109 A063261 * A062986 A291380 A280718

Adjacent sequences:  A131888 A131889 A131890 * A131892 A131893 A131894

KEYWORD

easy,nonn

AUTHOR

Jeffrey Barnett, Jul 24 2007

STATUS

approved

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Last modified August 21 06:54 EDT 2019. Contains 326162 sequences. (Running on oeis4.)