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A131893
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a(n) is the number of shapes of balanced trees with constant branching factor 7 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, 7, 21, 35, 35, 21, 7, 1, 49, 1029, 12005, 84035, 352947, 823543, 823543, 17294403, 155649627, 778248135, 2334744405, 4202539929, 4202539929, 1801088541, 21012699645, 105063498225, 291843050625, 486405084375, 486405084375, 270225046875, 64339296875
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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(7n+1+m) = (7 choose m) * a(n+1)^m * a(n)^(7-m), where n >= 0 and 0 <= m <= 7.
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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, 7, 'm'); binomial(7, m) *a(r+1)^m *a(r)^(7-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, 7];
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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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