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 1-3 of 3 results.

A086422 Duplicate of A046880.

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 1, 1, 2, 5, 7, 9, 24, 19, 35, 46, 86, 134, 187, 259, 450, 616, 823
Offset: 30

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Author

Keywords

A007894 Number of fullerenes with 2n vertices (or carbon atoms).

Original entry on oeis.org

1, 0, 1, 1, 2, 3, 6, 6, 15, 17, 40, 45, 89, 116, 199, 271, 437, 580, 924, 1205, 1812, 2385, 3465, 4478, 6332, 8149, 11190, 14246, 19151, 24109, 31924, 39718, 51592, 63761, 81738, 99918, 126409, 153493, 191839, 231017, 285914, 341658, 419013
Offset: 10

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Author

Boris Shraiman (boris(AT)physics.att.com), Gunnar Brinkmann and A. Dress (dress(AT)mathematik.uni-bielefeld.de)

Keywords

Comments

Enantiomorphic pairs are regarded as the same here. Cf. A057210.
Contradictory results from the program "buckygen" from Brinkmann et al. (2012) and the program "fullgen" from Brinkmann and Dress (1997) led to the detection of a non-algorithmic error in fullgen. This bug has now been fixed and the results are in complete agreement. a(10)-a(190) were independently confirmed by buckygen and fullgen, while a(191)-a(200) were computed only by buckygen. - Jan Goedgebeur, Aug 08 2012

References

  • A. T. Balaban, X. Liu, D. J. Klein, D. Babic, T. G. Schmalz, W. A. Seitz and M. Randic, "Graph invariants for fullerenes", J. Chem. Inf. Comput. Sci., vol. 35 (1995) 396-404.
  • M. Deza, M. Dutour and P. W. Fowler, Zigzags, railroads and knots in fullerenes, J. Chem. Inf. Comput. Sci., 44 (2004), 1282-1293.
  • J. L. Faulon, D. Visco and D. Roe, Enumerating Molecules, In: Reviews in Computational Chemistry Vol. 21, Ed. K. Lipkowitz, Wiley-VCH, 2005.
  • P. W. Fowler and D. E. Manolopoulos, An Atlas of Fullerenes, Cambridge Univ. Press, 1995, see p. 32.
  • P. W. Fowler, D. E. Manolopoulos and R. P. Ryan, "Isomerization of fullerenes", Carbon, 30 1235 1992.
  • A. M. Livshits and Yu. E. Lozovik, Cut-and-unfold approach to Fullerene enumeration, J. Chem. Inf. Comput. Sci., 44 (2004), 1517-1520.
  • Milicevic, A., and N. Trinajstic. "Combinatorial enumeration in chemistry." Chapter 8 in Chemical Modelling: Application and Theory, Vol. 4 (2006): 405-469.
  • M. Petkovsek and T. Pisanski, Counting disconnected structures: chemical trees, fullerenes, I-graphs and others, Croatica Chem. Acta, 78 (2005), 563-567.

Links

Crossrefs

Cf. A057210, A046880.

Formula

a(n) = (809/2612138803200)*sigma_9(n) + O(n^8) where sigma_9(n) is the ninth divisor power sum, cf. A013957. - Philip Engel, Nov 29 2017

Extensions

Corrected a(68)-a(100) and added a(101)-a(200). - Jan Goedgebeur, Aug 08 2012

A086423 Number of isolated-pentagon fullerenes with 2n vertices (or carbon atoms).

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 1, 1, 3, 6, 9, 12, 34, 33, 56, 78, 161, 252, 349, 483, 862, 1179, 1606, 2401, 3502, 4645, 6568, 8820, 11997, 16132, 21326, 27763, 37313, 46907, 61069, 78476, 99343, 124282, 158258, 196532, 242126, 301752, 372498, 449742
Offset: 30

Views

Author

N. J. A. Sloane, Sep 08 2003

Keywords

Comments

Enantiomorphic pairs are counted as different here. Cf. A046880.

References

  • P. W. Fowler and D. E. Manolopoulos, An Atlas of Fullerenes, Cambridge Univ. Press, 1995, see p. 33.

Links

Crossrefs

Cf. A046880, A007894, A057210.

Extensions

More terms from Gunnar Brinkmann, Aug 24 2006
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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