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A000913
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Number of bond-rooted polyenoids with n edges.
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1
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0, 1, 2, 12, 38, 143, 490, 1768, 6268, 22610, 81620, 297160, 1086172, 3991995, 14731290, 54587280, 202992808, 757398510, 2834493948, 10637507400, 40023577524, 150946230006, 570534370692, 2160865067312, 8199710635816
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| 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
| a(n)=(1/4)c(n+2)-(1/2)c(n+1)-(3/4)c((n+1)/2)+(1/2)c((n-1)/4), where c(n)=binomial(2n, n)/(n+1) are the Catalan numbers for n a nonnegative integer and 0 otherwise. G.f.=[ -4x+8x^2-sqrt(1-4x)+2xsqrt(1-4x)+3sqrt(1-4x^2)-2sqrt(1-4x^4)]/(8x^3). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 19 2004
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MAPLE
| c:=proc(n) if floor(n)=n then binomial(2*n, n)/(n+1) else 0 fi end:a:=n->(1/4)*c(n+2)-(1/2)*c(n+1)-(3/4)*c((n+1)/2)+(1/2)*c((n-1)/4):seq(a(n), n=1..27); (Deutsch)
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CROSSREFS
| Sequence in context: A192385 A185788 A035597 * A026575 A048349 A009632
Adjacent sequences: A000910 A000911 A000912 * A000914 A000915 A000916
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KEYWORD
| nonn
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AUTHOR
| E. K. Lloyd (E.K.Lloyd(AT)soton.ac.uk)
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 19 2004
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