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Search: id:A143657
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| A143657 |
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Number of 4-noncrossing stack-free partial matching without 1-arcs. |
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+0
1
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| 1, 1, 2, 5, 12, 32, 95, 301, 1001, 3495, 12708, 47932, 186581, 747619, 3073207
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OFFSET
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1,3
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COMMENT
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This sequence is the second row of Jin and Reidys table, p. 15; the first row, number of 3-noncrossing stack-free partial matching without 1-arcs, is A132441. Asymptotically a(n) ~ (1.217 * 10^7)*(n^(-21/2))*(3.0382^n).
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LINKS
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Emma Y. Jin and Christian M. Reidys, RNA-LEGO: Combinatorial Design of Pseudoknot RNA, Dec 4, 2007, arXiv:0711.1405.
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FORMULA
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a(n) = C_4(n,h) = SUM[b=0..{h-1}](-1)^{h-b-1}{h-1 Choose b}{T}_4(h-2h+2b+2,b+1); where the T function is defined in Jin and Reidys.
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CROSSREFS
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Cf. A132441.
Sequence in context: A148283 A002838 A076822 this_sequence A014326 A148284 A148285
Adjacent sequences: A143654 A143655 A143656 this_sequence A143658 A143659 A143660
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 28 2008
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EXTENSIONS
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Arxiv URL replaced by non-cached version - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 30 2009
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