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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 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 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}] (* Jean-François 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 Barnett, Jul 24 2007 STATUS approved

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