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A045906 Numbers of nonisomorphic systems of catafusenes (see Cyvin et al. (1994) for precise definition). 4
1, 1, 4, 12, 51, 205, 907, 4000, 18048, 81719, 373104, 1710740, 7882346, 36457711, 169252176, 788326910, 3683071949, 17255713627, 81056265252, 381668770108, 1801189604231, 8517995996495, 40360819400887, 191589552910532 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 28 02:07 EDT 2021. Contains 348307 sequences. (Running on oeis4.)