A045905 -id:A045905 - 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).

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, 1978, 825, 80, 4650, 8851, 4074, 473, 19819, 39481, 19902, 2517, 85710, 178043, 95920, 13431

Offset: 1

N. J. A. Sloane, Aug 15 2006

From Petros Hadjicostas, May 25 2019: (Start)
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.
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).
The rows of the table are indexed by the total number of hexagons in the appendages.
(End)

			The table begins:
     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, 1978,  825,  80;
  4650, 8851, 4074, 473;
  ...

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.

Columns give A044045, A045903 - A045905. Row sums give A045906.

Corrected by N. J. A. Sloane, Apr 14 2013 (thanks to Michel Marcus for noticing that something was wrong)
Name edited by Petros Hadjicostas, May 25 2019
More terms from reference from Petros Hadjicostas, May 25 2019

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

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).

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