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%I #33 Mar 27 2021 03:49:21
%S 1,1,4,12,51,205,907,4000,18048,81719,373104,1710740,7882346,36457711,
%T 169252176,788326910,3683071949,17255713627,81056265252,381668770108,
%U 1801189604231,8517995996495,40360819400887,191589552910532
%N Numbers of nonisomorphic systems of catafusenes (see Cyvin et al. (1994) for precise definition).
%C Row sums of table in A121178.
%C 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
%H S. J. Cyvin, B. N. Cyvin, J. Brunvoll and E. Brendsdal, <a href="https://doi.org/10.1021/ci00021a026">Enumeration and Classification of Certain Polygonal Systems Representing Polycyclic Conjugated Hydrocarbons: Annelated Catafusenes</a>, Journal of Chemical Information and Modeling [formerly, J. Chem. Inform. Comput. Sci.], 34 (1994), pp. 1174-1180.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Fusene.html">Fusene</a>.
%F 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]
%F a(n) = A038392(n+1) + A045903(n) + A045904(n) + A045905(n). - _Sean A. Irvine_, Mar 26 2021
%Y Cf. A121178.
%Y Cf. A038392, A045903, A045904, A045905.
%K nonn
%O 0,3
%A _N. J. A. Sloane_
%E More terms from _Emeric Deutsch_, Mar 13 2004
%E Name edited by _Petros Hadjicostas_, May 25 2019
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