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A038392
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Mono-4-polyhexes.
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2
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1, 1, 2, 6, 19, 71, 274, 1117, 4650, 19819, 85710, 375712, 1664203, 7439593, 33515758, 152019560, 693625265, 3181528275, 14661581030, 67850297506, 315187646601, 1469195636293, 6869889703638, 32215399021901
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| J. Brunvoll et al., Studies of some chemically relevant polygonal systems: mono-q-polyhexes, ACH Models in Chem., 133 (3) (1996), 277-298, Eq 16.
B. N. Cyvin et al., A class of polygonal systems representing polycyclic conjugated hydrocarbons ..., Monat. f. Chemie, 125 (1994), 1327-1337.
S. J. Cyvin et al., Graph-theoretical studies on fluoranthenoids and fluorenoids..., J. Molec. Struct. (Theochem), 285 (1993), 179-185.
S. J. Cyvin et al., Enumeration and classification of certain polygonal systems...: annelated catafusenes, J. Chem. Inform. Comput. Sci., 34 (1994), 1174-1180.
F. Harary and R. C. Read, The enumeration of tree-like polyhexes, Proc. Edinb. Math. Soc. (2) 17 (1970), 1-13.
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FORMULA
| G.f.: [2(1-z^2)-(1-z)f(z)-f(z^2)]/[4(1-z)] where f(z)=sqrt(1-6z+5z^2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 14 2004
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MATHEMATICA
| f[z_] := Sqrt[5*z^2 - 6*z + 1]; g[z_] := (2*(1 - z^2) - (1-z)*f[z] - f[z^2])/ (4*(1-z)); Drop[ CoefficientList[ Series[ g[z], {z, 0, 24}], z], 1] (* From Jean-François Alcover, Oct 13 2011, after Emeric Deutsch *)
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CROSSREFS
| Apart from initial term, (A002212+A007317)/2. See A044045 for another version.
Sequence in context: A150116 A150117 * A044045 A150118 A150119 A181770
Adjacent sequences: A038389 A038390 A038391 * A038393 A038394 A038395
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 14 2004
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