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A086521
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Number of tandem duplication trees on n duplicated genes. For n > 2, 2a(n) is the number of rooted tandem duplication trees.
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0
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1, 1, 3, 11, 46, 210, 1021, 5202, 27477, 149324, 830357, 4705386, 27087106, 158019030, 932390694, 5555902302, 33391080001, 202196156448, 1232550473918, 7558030268270, 46592437224093, 288599067239678, 1795348952256896
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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REFERENCES
| O. Gascuel, M. Hendy, A. Jean-Marie and R.McLachlan, (2003) The combinatorics of tandem duplication trees, Systematic Biology 52, 110-118.
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LINKS
| Author?, More information
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FORMULA
| a(n)=b(n+1, n-1), where b(n, 0)=b(n-1, 0)+b(n-1, 1); b(n, k)=b(n-1, k+1)+b(n, k-1), for k=1, ..., n-2; with initial values b(2, 0)=1, b(3, 0)=0, b(3, 1)=1.
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EXAMPLE
| a(5)=11, so there are 11 binary leaf labeled trees on 5 duplicate genes. As there are 15 binary leaf labeled trees, this means not all binary leaf labeled trees can represent a gene duplication tree.
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CROSSREFS
| Sequence in context: A155134 A006605 A193074 * A046996 A129579 A030814
Adjacent sequences: A086518 A086519 A086520 * A086522 A086523 A086524
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KEYWORD
| nonn
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AUTHOR
| Michael D Hendy (m.hendy(AT)massey.ac.nz), Sep 10 2003
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EXTENSIONS
| More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Mar 11 2005
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