A045904 -id:A045904 - cp's OEIS frontend

A045906 Numbers of nonisomorphic systems of catafusenes (see Cyvin et al. (1994) for precise definition).

1, 1, 4, 12, 51, 205, 907, 4000, 18048, 81719, 373104, 1710740, 7882346, 36457711, 169252176, 788326910, 3683071949, 17255713627, 81056265252, 381668770108, 1801189604231, 8517995996495, 40360819400887, 191589552910532

Offset: 0

N. J. A. Sloane

nonn

Row sums of table in A121178.

These are the row sums in Table 5 (p. 1179) of Cyvin et al. (1994), which lists the total number of nonisomorphic systems of catafusenes classified according to the numbers alpha of appendages to the core and the total numbers a of hexagons in the appendages (not including any possible hexagons in the core). - Petros Hadjicostas, May 25 2019

S. J. Cyvin, B. N. Cyvin, J. Brunvoll and E. Brendsdal, Enumeration and Classification of Certain Polygonal Systems Representing Polycyclic Conjugated Hydrocarbons: Annelated Catafusenes, Journal of Chemical Information and Modeling [formerly, J. Chem. Inform. Comput. Sci.], 34 (1994), pp. 1174-1180.
Eric Weisstein's World of Mathematics, Fusene.

Cf. A121178.

Cf. A038392, A045903, A045904, A045905.

G.f.: (8*(1+x^2-6*x^3-x^4) - (1-3*x)*(1-x)^(5/2)*(1-5*x)^(1/2) - (1-x)^(-1)*(5+3*x-5*x^2-7*x^3)*(1-x^2)^(1/2)*(1-5*x^2)^(1/2) - 2*(1-x^4)^(1/2)*(1-5*x^4)^(1/2))/16/x^4. - Emeric Deutsch, Mar 13 2004. [This g.f. is (essentially) Eq. (48) on p. 1179 in the Cyvin et al. (1994) paper. - N. J. A. Sloane, Apr 14 2013]

a(n) = A038392(n+1) + A045903(n) + A045904(n) + A045905(n). - Sean A. Irvine, Mar 26 2021

More terms from Emeric Deutsch, Mar 13 2004

Name edited by Petros Hadjicostas, May 25 2019

A044046 Nonisomorphic catacondensed monoheptafusenes (see reference for precise definition).

Original entry on oeis.org

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

N. J. A. Sloane

nonn

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.

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

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

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)

More terms from Emeric Deutsch, Mar 14 2004

More terms from Michel Marcus, Apr 22 2019

A121070 Nonisomorphic catacondensed monoheptafusenes (see reference for precise definition).

Original entry on oeis.org

1, 1, 4, 13, 56, 234, 1034, 4570, 20492, 92329, 418896

Offset: 0

N. J. A. Sloane, Aug 10 2006

nonn

B. N. Cyvin et al., A class of polygonal systems representing polycyclic conjugated hydrocarbons ..., Monat. f. Chemie, 125 (1994), 1327-1337 (see Table 1).

Equals sum of columns of triangle whose successive columns are A000007, A044045, A121071, A045904, ...

cp's OEIS Frontend

A045906 Numbers of nonisomorphic systems of catafusenes (see Cyvin et al. (1994) for precise definition).

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A044046 Nonisomorphic catacondensed monoheptafusenes (see reference for precise definition).

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A121070 Nonisomorphic catacondensed monoheptafusenes (see reference for precise definition).

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