A038392 -id:A038392 - cp's OEIS frontend

A044045 Same as A038392 except for initial term.

0, 1, 2, 6, 19, 71, 274, 1117, 4650, 19819, 85710, 375712, 1664203, 7439593, 33515758, 152019560, 693625265, 3181528275, 14661581030, 67850297506, 315187646601, 1469195636293, 6869889703638, 32215399021901, 151467334017864, 713881817440421, 3372142139764434

Offset: 0

N. J. A. Sloane

nonn

B. N. Cyvin, E. Brendsdal, J. Brunvoll, S. J. Cyvin, A class of polygonal systems representing polycyclic conjugated hydrocarbons: Catacondensed monoheptafusenes, Monat. f. Chemie, 125 (1994), 1327-1337.
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.
F. Harary and R. C. Read, The enumeration of tree-like polyhexes, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.
Eric W. Weisstein, Fusene, MathWorld-A Wolfram Web Resource.

Cf. A121178.

G.f.: (2*(1-z)^2 - (1-z)*f(z) - f(z^2))/(4*z*(1-z)) where f(z) = sqrt(1 - 6z + 5z^2). - Emeric Deutsch, Mar 14 2004

More terms from Emeric Deutsch, Mar 14 2004

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

Original entry on oeis.org

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

A046697 Number of catacondensed simply-connected monopentapolyhexes (catafusenes).

Original entry on oeis.org

1, 1, 3, 9, 35, 137, 574, 2431, 10534, 46123, 204343, 912967, 4111375, 18637303, 84988775, 389589095, 1794280695, 8298536715, 38527147681, 179487103411, 838820394913, 3931498654243, 18475619837816, 87036536948489, 410947150379120, 1944378509186237

Offset: 1

N. J. A. Sloane

nonn

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.

Cf. A024311, A038392, A044046.

a(n) = A038392(n) + A044046(n).

More terms from Sean A. Irvine, Apr 16 2021

cp's OEIS Frontend

A044045 Same as A038392 except for initial term.

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

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Author

Keywords

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Formula

Extensions

A046697 Number of catacondensed simply-connected monopentapolyhexes (catafusenes).

Views

Author

Keywords

Links

Crossrefs

Formula

Extensions