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Search: id:A045890
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| A045890 |
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Catafusenes (see reference for precise definition). |
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1
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| 1, 3, 12, 49, 204, 864, 3714, 16170, 71178, 316303, 1417248, 6396273, 29051856, 132700725, 609200640, 2809373915, 13008512040, 60457182345, 281919911460, 1318666411635, 6185356518660, 29088241615910, 137121834221346
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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3-fold convolution of A002212. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 13 2004
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REFERENCES
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S. J. Cyvin et al., Enumeration and classification of certain polygonal systems...: annelated catafusenes, J. Chem. Inform. Comput. Sci., 34 (1994), 1174-1180.
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FORMULA
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G.f.: [1-x-sqrt(1-6x+5x^2)]^3/(8x^3). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 13 2004
a(n)=(3/n)*sum(binomial(n, j)*binomial(2j+2, j-1), j=1..n) for n>=1. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 25 2004
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MAPLE
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a := n->(3/n)*sum(binomial(n, j)*binomial(2*j+2, j-1), j=1..n): 1, seq(a(n), n=1..22);
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CROSSREFS
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Cf. A002212.
Sequence in context: A037646 A012772 A012864 this_sequence A049673 A052703 A002179
Adjacent sequences: A045887 A045888 A045889 this_sequence A045891 A045892 A045893
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KEYWORD
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nonn
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AUTHOR
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njas
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 13 2004
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