A044046 Nonisomorphic catacondensed monoheptafusenes (see reference for precise definition).
0, 0, 1, 3, 16, 66, 300, 1314, 5884, 26304, 118633, 537255, 2447172, 11197710, 51473017, 237569535, 1100655430, 5117008440, 23865566651, 111636805905, 523632748312, 2462303017950, 11605730134178, 54821137926588, 259479816361256, 1230496691745816, 5845551200648015
Offset: 0
Keywords
Links
- S. J. Cyvin, J. Brunvoll, and B. N. Cyvin, Harary-Read numbers for catafusenes: Complete classification according to symmetry, Journal of mathematical chemistry 9.1 (1992): 19-31.
- S. J. Cyvin, J. Brunvoll, Generating functions for the Harary-Read numbers classified according to symmetry, Journal of mathematical chemistry 9.1 (1992): 33-38.
- B. N. Cyvin et al., A class of polygonal systems representing polycyclic conjugated hydrocarbons: Catacondensed monoheptafusenes, Monat. f. Chemie, 125 (1994), 1327-1337 (see Table 1).
- S. J. Cyvin et al., Graph-theoretical studies on fluoranthenoids and fluorenoids:enumeration of some catacondensed systems, J. Molec. Struct. (Theochem), 285 (1993), 179-185.
- S. J. Cyvin et al., Enumeration and Classification of Certain Polygonal Systems Representing Polycyclic Conjugated Hydrocarbons: Annelated Catafusenes, J. Chem. Inform. Comput. Sci., 34 (1994), 1174-1180.
- F. Harary and R. C. Read, The enumeration of tree-like polyhexes, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.
Programs
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PARI
U(z)= (1-3*z-sqrt(1-6*z+5*z^2))/(2*z); my(x='x + O('x^40)); concat([0, 0], Vec((U(z)^2 + U(z^2))/2)) \\ Michel Marcus, Apr 22 2019
Formula
From Emeric Deutsch, Mar 14 2004: (Start)
G.f.: (U(z)^2 + U(z^2))/2, where U(z) = (1 - 3z - sqrt(1 - 6z + 5z^2))/(2z). [corrected by Michel Marcus, Apr 22 2019]
Extensions
More terms from Emeric Deutsch, Mar 14 2004
More terms from Michel Marcus, Apr 22 2019