cp's OEIS Frontend

A121178 Four-column table read by rows: number of nonisomorphic systems of catafusenes in an example (see Cyvin et al. (1994) for precise definition).

%I A121178 #63 Jul 09 2025 04:09:16
%S A121178 1,0,0,0,2,2,0,0,6,5,1,0,19,26,5,1,71,101,31,2,274,457,160,16,1117,
%T A121178 1978,825,80,4650,8851,4074,473,19819,39481,19902,2517,85710,178043,
%U A121178 95920,13431
%N A121178 Four-column table read by rows: number of nonisomorphic systems of catafusenes in an example (see Cyvin et al. (1994) for precise definition).
%C A121178 From _Petros Hadjicostas_, May 25 2019: (Start)
%C A121178 The sequence (a rectangular array) refers to Table 5 on p. 1179 of Cyvin et al. (1994). The zeroth row and the zeroth column from Table 5 do not appear in this sequence. The columns (alpha = 1, 2, 3, 4) refer to the number of appendages to the core.
%C A121178 The table refers to the example described on pp. 1177-1179 of the paper and especially to Figure 5 (p. 1178). The entries refer to the number of nonisomorphic systems of catafusenes in this example (as shown in Figure 5, p. 1178).
%C A121178 The rows of the table are indexed by the total number of hexagons in the appendages.
%C A121178 (End)
%H A121178 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 A121178 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Fusene.html">Fusene</a>.
%e A121178 The table begins:
%e A121178      1,    0,    0,   0;
%e A121178      2,    2,    0,   0;
%e A121178      6,    5,    1,   0;
%e A121178     19,   26,    5,   1;
%e A121178     71,  101,   31,   2;
%e A121178    274,  457,  160,  16;
%e A121178   1117, 1978,  825,  80;
%e A121178   4650, 8851, 4074, 473;
%e A121178   ...
%Y A121178 Columns give A044045, A045903 - A045905. Row sums give A045906.
%K A121178 nonn,tabf
%O A121178 1,5
%A A121178 _N. J. A. Sloane_, Aug 15 2006
%E A121178 Corrected by _N. J. A. Sloane_, Apr 14 2013 (thanks to _Michel Marcus_ for noticing that something was wrong)
%E A121178 Name edited by _Petros Hadjicostas_, May 25 2019
%E A121178 More terms from reference from _Petros Hadjicostas_, May 25 2019