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

0,3

Comments

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

Links

Table of n, a(n) for n=0..23.

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.

Formula

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

Crossrefs

Cf. A121178.

Cf. A038392, A045903, A045904, A045905.

Sequence in context: A149400 A149401 A149402 * A025282 A303392 A149403

Adjacent sequences: A045903 A045904 A045905 * A045907 A045908 A045909

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Emeric Deutsch, Mar 13 2004

Name edited by Petros Hadjicostas, May 25 2019

Status

approved