A045906 -id:A045906 - 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

A045909 Number of unsymmetrical catafusenes with n hexagons (see reference for precise definition).

Original entry on oeis.org

0, 0, 1, 8, 39, 190, 861, 3943, 17867, 81496, 372378, 1709842, 7879360, 36454004, 169239651, 788311290, 3683018475, 17255646688, 81056033636, 381668479192, 1801188588566, 8517994717214, 40360814900566, 191589547228523, 911009396044132, 4338777661726040

Offset: 0

N. J. A. Sloane

nonn

Column C_s of Table 6 in Cyvin et al. Computed by subtracting all the other symmetry classes from the total. - Sean A. Irvine, Mar 27 2021

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.

Cf. A045906, A045907, A045908, A342554, A342570, A030529, A055879.

a(n) = A045906(n) - A045907(n) - A045908(n/2) - A342554(n/2) - A342570(n/2) - 2*A030529(n/4) - A055879(n/4) - [n=0] with sequences assumed to be 0 for non-integer arguments. - Sean A. Irvine, Mar 27 2021

More terms from Sean A. Irvine, Mar 27 2021

A342554 Number of catafusenes with 2n hexagons and C symmetry.

Original entry on oeis.org

0, 0, 1, 5, 22, 97, 408, 1752, 7535, 32895, 144816, 644058, 2886967, 13037352, 59248959, 270799903, 1243939278, 5740014143, 26594306442, 123668622726, 577003771681, 2700346810482, 12672753684799, 59625966523555, 281207237408728, 1329130156859362

Offset: 0

Sean A. Irvine, Mar 27 2021

nonn

Column C in Table 6 and Eq. (52) in Cyvin et al.

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.

Cf. A045906, A045907, A045908, A045909, A342570.

a(n) = (1/4) * (A002212(n+1) - A002212(n) - A039658(n)) - (1/2) * (A055879(n) + A002212(n/2) - A055879(n/2)) where sequences are assumed 0 for non-integer arguments.

A342570 Number of catafusenes with 2n hexagons and D_{2h}(a) symmetry.

Original entry on oeis.org

0, 1, 1, 3, 4, 9, 13, 29, 46, 101, 167, 375, 644, 1461, 2563, 5899, 10534, 24469, 44237, 103643, 189302, 446381, 821905, 1948853, 3612868, 8605289, 16044151, 38362199, 71877226, 172423769, 324440379, 780496109, 1474118424, 3554991269, 6736507309, 16281079899

Offset: 0

Sean A. Irvine, Mar 27 2021

nonn

Column D_{2h}(a) in Table 6 and Eq. (51) in Cyvin et al.

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.

Cf. A045906, A045907, A045908, A045909, A342554.

a(n) = A055879(n) + (1/2) * (A039658(n) - A055879(n/2)) where A055879 is 0 for non-integer arguments.

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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A045909 Number of unsymmetrical catafusenes with n hexagons (see reference for precise definition).

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A342554 Number of catafusenes with 2n hexagons and C symmetry.

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A342570 Number of catafusenes with 2n hexagons and D_{2h}(a) symmetry.

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