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A044046
Nonisomorphic catacondensed monoheptafusenes (see reference for precise definition).
2
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
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.
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
Sequence in context: A359176 A062960 A293579 * A179600 A278089 A248016
KEYWORD
nonn
EXTENSIONS
More terms from Emeric Deutsch, Mar 14 2004
More terms from Michel Marcus, Apr 22 2019
STATUS
approved