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Search: id:A121133
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| A121133 |
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Numbers of isomers of unbranched a-4-catapolypentagons - see Brunvoll reference for precise definition. |
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4
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| 1, 1, 2, 3, 8, 16, 38, 80, 180, 384, 840, 1792, 3856, 8192, 17440, 36864, 77888, 163840, 344192, 720896, 1507584, 3145728, 6554112, 13631488, 28312576, 58720256, 121636864, 251658240, 520097792, 1073741824, 2214600704, 4563402752
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Numbers of polypentagons with two connected internal vertices.
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REFERENCES
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J. Brunvoll, S. J. Cyvin and B. N. Cyvin, Isomer enumeration of polygonal systems..., J. Molec. Struct. (Theochem), 364 (1996), 1-13.
S. J. Cyvin et al., Theory of polypentagons, J. Chem. Inf. Comput. Sci., 33 (1993), 466-474.
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LINKS
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J. Brunvoll, S. J. Cyvin and B. N. Cyvin, Isomer enumeration of polygonal systems..., J. Molec. Struct. (Theochem), 364 (1996), 1-13, Table 10.
S. J. Cyvin et al., Theory of polypentagons, J. Chem. Inf. Comput. Sci., 33 (1993), 466-474.
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MAPLE
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H := proc(r, alpha, q) local rhalf, alphahalf ; rhalf := floor(r/2) ; alphahalf := floor(alpha/2) ; (binomial(rhalf-1, alphahalf-1)*(q-3)+binomial(rhalf-1, alphahalf))*(q-3)^(rhalf-alphahalf-1) ; end:
J := proc(r, alpha, q) (binomial(r-2, alpha-2)*(q-3)^2+2*binomial(r-2, alpha-1)*(q-3)+binomial(r-2, alpha))*(q-3)^(r-alpha-2) ; end: Ifunc := proc(r, alpha, q) J(r, alpha, q)/4+binomial(2, r-alpha)/4+ (1+(-1)^(r+alpha)+(1+(-1)^alpha)*(1-(-1)^r)/2)*H(r, alpha, q)/4 ; end:
A121133 := proc(n) if n = 1 then 1; else Ifunc(n, 1, 5) ; fi ; end: for n from 1 to 80 do printf("%d, ", A121133(n)) ; od: # R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 07 2008
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KEYWORD
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nonn,new
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AUTHOR
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njas, Aug 13 2006, Sep 24 2006
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EXTENSIONS
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Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 07 2008
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