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

0,4

Links

Table of n, a(n) for n=0..26.

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.

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)

Prog

(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

Crossrefs

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

Sequence in context: A359176 A062960 A293579 * A179600 A278089 A248016

Adjacent sequences: A044043 A044044 A044045 * A044047 A044048 A044049

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Emeric Deutsch, Mar 14 2004

More terms from Michel Marcus, Apr 22 2019

Status

approved