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A131890 a(n) is the number of shapes of balanced trees with constant branching factor 4 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, 4, 6, 4, 1, 16, 96, 256, 256, 1536, 3456, 3456, 1296, 3456, 3456, 1536, 256, 256, 96, 16, 1, 64, 1536, 16384, 65536, 1572864, 14155776, 56623104, 84934656, 905969664, 3623878656, 6442450944, 4294967296, 17179869184, 25769803776, 17179869184, 4294967296 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1365

Jeffrey Barnett, Counting Balanced Tree Shapes

FORMULA

a(0) = a(1) = 1; a(4n+1+m) = (4 choose m) * a(n+1)^m * a(n)^(4-m), where n >= 0 and 0 <= m <= 4.

MAPLE

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

      r:= iquo(n-1, 4, 'm'); binomial(4, m) *a(r+1)^m *a(r)^(4-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, 4];

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

CROSSREFS

Cf. A110316, A131889, A131891, A131892, A131893.

Column k=4 of A221857. - Alois P. Heinz, Apr 17 2013

Sequence in context: A010670 A240444 A199358 * A062751 A135911 A164356

Adjacent sequences:  A131887 A131888 A131889 * A131891 A131892 A131893

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.)