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

Author

N. J. A. Sloane

Keywords

• nonn

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.

Crossrefs

Cf. A002212, A045445, A045904, A121070. Equals A121071/2.

Programs

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]

a(2n) = (1/2)*(A045445(2n) + A002212(n)), n >= 1; a(2n+1) = (1/2)*A045445(2n+1), n >= 0. (End)

Extensions

More terms from Emeric Deutsch, Mar 14 2004

More terms from Michel Marcus, Apr 22 2019