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A131892
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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.
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6
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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
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0,3
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LINKS
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FORMULA
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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.
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MAPLE
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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:
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MATHEMATICA
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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];
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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