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A000235
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Number of n-node rooted trees of height 3.
(Formerly M2732 N1097)
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17
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0, 0, 0, 1, 3, 8, 18, 38, 76, 147, 277, 509, 924, 1648, 2912, 5088, 8823, 15170, 25935, 44042, 74427, 125112, 209411, 348960, 579326, 958077, 1579098, 2593903, 4247768, 6935070, 11290627, 18330973, 29684082, 47946852, 77258764, 124198083
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| (1, 1, 2, 3, 5, 8,...) convolved with (0, 0, 1, 2, 4, 7,...) = (0, 0, 1, 3, 8,...) [From Gary W. Adamson, Aug 14 2010]
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REFERENCES
| J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| N. J. A. Sloane, Table of n, a(n) for n=1..200
N. J. A. Sloane, Maple programs for counting rooted trees by height (after Riordan)
Index entries for sequences related to rooted trees
Index entries for sequences related to trees
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FORMULA
| a(n) = A001383(n) - A000041(n-1). [Christian G. Bower].
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MAPLE
| For Maple program see link.
ZL:=proc(m) local i; [T0, {seq(T.i=Prod(Z, Set(T.(i+1))), i=0..m-1), T.m=Z}, unlabeled] end:A000235:=n -> count(ZL(3), size=n)-count(ZL(2), size=n): seq(A000235(n), n=1..36); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 23 2007
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MATHEMATICA
| m = 36; Rest @ CoefficientList[ Series[x*Product[(1-x^k)^(-PartitionsP[k-1]), {k, 1, m}], {x, 0, m}], x] - PartitionsP[Range[0, m-1]] (* From Jean-François Alcover, Jul 05 2011, after C. G. Bower *)
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CROSSREFS
| Sequence in context: A000713 A078409 A036642 * A006478 A104187 A051633
Adjacent sequences: A000232 A000233 A000234 * A000236 A000237 A000238
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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