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A316624
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Number of balanced p-trees with n leaves.
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12
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1, 1, 1, 2, 2, 4, 4, 8, 9, 16, 20, 40, 47, 83, 111, 201, 259, 454, 603, 1049, 1432, 2407, 3390, 6006, 8222, 13904, 20304, 34828, 50291, 85817, 126013, 217653, 317894, 535103, 798184, 1367585, 2008125, 3360067, 5048274, 8499942, 12623978, 21023718, 31552560, 52575257
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OFFSET
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1,4
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COMMENTS
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A p-tree of weight n is either a single node (if n = 1) or a finite sequence of p-trees whose weights are weakly decreasing and sum to n.
A tree is balanced if all leaves have the same height.
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LINKS
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EXAMPLE
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The a(1) = 1 through a(7) = 4 balanced p-trees:
o (oo) (ooo) (oooo) (ooooo) (oooooo) (ooooooo)
((oo)(oo)) ((ooo)(oo)) ((ooo)(ooo)) ((oooo)(ooo))
((oooo)(oo)) ((ooooo)(oo))
((oo)(oo)(oo)) ((ooo)(oo)(oo))
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MATHEMATICA
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ptrs[n_]:=If[n==1, {"o"}, Join@@Table[Tuples[ptrs/@p], {p, Rest[IntegerPartitions[n]]}]];
Table[Length[ptrs[n]], {n, 12}]
Table[Length[Select[ptrs[n], SameQ@@Length/@Position[#, "o"]&]], {n, 12}]
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PROG
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(PARI) seq(n)={my(p=x + O(x*x^n), q=0); while(p, q+=p; p = 1/prod(k=1, n, 1 - polcoef(p, k)*x^k + O(x*x^n)) - 1 - p); Vec(q)} \\ Andrew Howroyd, Oct 26 2018
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CROSSREFS
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Cf. A000311, A000669, A001678, A005804, A048816, A079500, A119262, A120803, A141268, A196545, A289501, A319312.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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