cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

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

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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

Crossrefs

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

Extensions

More terms from Emeric Deutsch, Mar 13 2004
Name edited by Petros Hadjicostas, May 25 2019

A044045 Same as A038392 except for initial term.

Original entry on oeis.org

0, 1, 2, 6, 19, 71, 274, 1117, 4650, 19819, 85710, 375712, 1664203, 7439593, 33515758, 152019560, 693625265, 3181528275, 14661581030, 67850297506, 315187646601, 1469195636293, 6869889703638, 32215399021901, 151467334017864, 713881817440421, 3372142139764434
Offset: 0

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Crossrefs

Cf. A121178.

Formula

G.f.: (2*(1-z)^2 - (1-z)*f(z) - f(z^2))/(4*z*(1-z)) where f(z) = sqrt(1 - 6z + 5z^2). - Emeric Deutsch, Mar 14 2004

Extensions

More terms from Emeric Deutsch, Mar 14 2004

A045904 Nonisomorphic catacondensed monoheptafusenes (see reference for precise definition).

Original entry on oeis.org

0, 0, 0, 1, 5, 31, 160, 825, 4074, 19902, 95920
Offset: 0

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References

  • B. N. Cyvin et al., A class of polygonal systems representing polycyclic conjugated hydrocarbons ..., Monat. f. Chemie, 125 (1994), 1327-1337 (see Table 1).
  • S. J. Cyvin et al., Enumeration and classification of certain polygonal systems... : annelated catafusenes, J. Chem. Inform. Comput. Sci., 34 (1994), 1174-1180.

Crossrefs

3rd column of A121178.

A045903 Number of nonisomorphic systems of catafusenes in an example in Cyvin et al. (1994) with two appendages to the core indexed by the total number of hexagons in the appendages.

Original entry on oeis.org

0, 0, 2, 5, 26, 101, 457, 1978, 8851, 39481, 178043
Offset: 0

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From Petros Hadjicostas, May 25 2019: (Start)
This is column alpha = 2 in Table 5 on p. 1179 of Cyvin et al. (1994). (The table starts with column alpha = 0.) Here, the index alpha for the columns in Table 5 is 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 Table 5 are indexed by the total number of hexagons in the appendages.
Therefore, a(n) = number of nonisomorphic systems of catefusenes in the example on pp. 1177-1179 of Cyvin et al. (1994) with alpha = 2 appendages to the core, where n = total number of hexagons in the appendages.
From Note 10 (p. 1180) in Cyvin et al. (1994), we see that (most probably) the number of hexagons a (= n in this sequence) does not include any hexagons in the core.
(End)

Crossrefs

Cf. A121178.

Extensions

Name edited by Petros Hadjicostas, May 25 2019

A045905 Catafusenes (see reference for precise definition).

Original entry on oeis.org

0, 0, 0, 0, 1, 2, 16, 80, 473, 2517, 13431, 69357, 353943, 1780894, 8886254, 44024308, 217021967, 1065653519, 5217704239, 25491204743, 124335254416, 605720277647, 2948274685881, 14341442951945, 69732440151924
Offset: 0

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References

  • S. J. Cyvin et al., Enumeration and classification of certain polygonal systems... : annelated catafusenes, J. Chem. Inform. Comput. Sci., 34 (1994), 1174-1180, ^4O = ^4F_7 page 1178.

Crossrefs

Last column of A121178.

Formula

8*a(n) = A045829(n) + 3*A045445(n/2) + 2*A002212(n/4) + 2*A039660(n) for n > 0, where sequence values with non-integer index are implicitly defined as 0. - R. J. Mathar, Jul 30 2019
Showing 1-5 of 5 results.