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 A131889 a(n) is the number of shapes of balanced trees with constant branching factor 3 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, 3, 3, 1, 9, 27, 27, 81, 81, 27, 27, 9, 1, 27, 243, 729, 6561, 19683, 19683, 59049, 59049, 19683, 177147, 531441, 531441, 1594323, 1594323, 531441, 531441, 177147, 19683, 59049, 59049, 19683, 19683, 6561, 729, 243, 27, 1, 81, 2187, 19683, 531441, 4782969 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) is always an integer power of 3. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1093 Jeffrey Barnett, Counting Balanced Tree Shapes. FORMULA a(0) = a(1) = 1; a(3n+1+m) = (3 choose m) * a(n+1)^m * a(n)^(3-m), where n >= 0 and 0 <= m <= 3. MAPLE a:= proc(n) option remember; local m, r; if n<2 then 1 else       r:= iquo(n-1, 3, 'm'); binomial(3, m) *a(r+1)^m *a(r)^(3-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, 3]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jun 04 2018, after Alois P. Heinz *) CROSSREFS Cf. A110316, A131890, A131891, A131892, A131893. Column k=3 of A221857. - Alois P. Heinz, Apr 17 2013 Sequence in context: A157401 A143911 A185422 * A292386 A174287 A186826 Adjacent sequences:  A131886 A131887 A131888 * A131890 A131891 A131892 KEYWORD easy,nonn,look 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.)