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Search: id:A000912
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| A000912 |
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Expansion of (sqrt(1-4x^2)-sqrt(1-4x))/(2x). |
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+0
2
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| 1, 0, 2, 4, 14, 40, 132, 424, 1430, 4848, 16796, 58744, 208012, 742768, 2674440, 9694416, 35357670, 129643360, 477638700, 1767258328, 6564120420, 24466250224, 91482563640, 343059554864, 1289904147324, 4861946193440, 18367353072152
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of bond-rooted polyenoids with 2n-1 edges.
Partial sums are A129366.
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REFERENCES
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S. J. Cyvin, J. Brunvoll, E. Brendsdal, B. N. Cyvin and E. K. Lloyd, Enumeration of polyene hydrocarbons: a complete mathematical solution, J. Chem. Inf. Comput. Sci., 35 (1995) 743-751
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FORMULA
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a(n)=C(n) if n is even and a(n)=C(n)-C((n-1)/2) if n is odd, where C(n)=binom(2n, n)/(n+1) are the Catalan numbers (A000108). a(n)=2*A000150(n) for n>0. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 19 2004
G.f.: c(x)-x*c(x^2), where c(x) = g.f. for A000108; a(n)=C(n)-C((n-1)/2)(1-(-1)^n)/2, C(n)=A000108(n). - Paul Barry (pbarry(AT)wit.ie), Apr 11 2007
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MAPLE
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c:=n->binomial(2*n, n)/(n+1):a:=proc(n) if n mod 2 = 1 then c(n+1) else c(n+1)-c(n/2) fi end: seq(a(n), n=0..28); (Deutsch)
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CROSSREFS
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Sequence in context: A006252 A079995 A152011 this_sequence A128750 A047152 A007866
Adjacent sequences: A000909 A000910 A000911 this_sequence A000913 A000914 A000915
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KEYWORD
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nonn
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AUTHOR
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E. K. Lloyd (E.K.Lloyd(AT)soton.ac.uk)
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 19 2004
Edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 02 2008 at the suggestion of R. J. Mathar
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