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A036662
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Shapes of height-balanced AVL trees of height at most 5 with n nodes.
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3
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0, 1, 1, 2, 1, 4, 6, 4, 17, 32, 44, 60, 70, 184, 476, 872, 1553, 2720, 4288, 6312, 9004, 11992, 14372, 15400, 14630, 11968, 8104, 4376, 1820, 560, 120, 16, 1
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OFFSET
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0,4
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REFERENCES
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F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 239, Eq 79, A_5.
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LINKS
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FORMULA
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MAPLE
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a:= proc(n) local B, z; B:= proc(x, y, d) if d>=1 then x+B(x^2+2*x*y, x, d-1) else x fi end; coeff(B(z, 0, 5), z, n) end: seq(a(n), n=0..32); # Alois P. Heinz, Aug 27 2008
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MATHEMATICA
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a[n_] := Module[{B, z}, B[x_, y_, d_] := If[d >= 1, x+B[x^2+2*x*y, x, d-1], x]; Coefficient[B[z, 0, 5], z, n]]; Table[a[n], {n, 0, 32}] (* Jean-François Alcover, Feb 24 2015, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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