login
Number of isolated-pentagon (IPR) fullerenes with 2n vertices (or carbon atoms).
4

%I #29 Oct 06 2022 16:13:34

%S 1,0,0,0,0,1,1,1,2,5,7,9,24,19,35,46,86,134,187,259,450,616,823,1233,

%T 1799,2355,3342,4468,6063,8148,10774,13977,18769,23589,30683,39393,

%U 49878,62372,79362,98541,121354,151201,186611,225245,277930,335569

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

%C Enantiomorphic pairs are regarded as the same here. Cf. A086423.

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

%H Jan Goedgebeur, <a href="/A046880/b046880.txt">Table of n, a(n) for n = 30..200</a>, terms a(30)..a(120) from Gunnar Brinkmann.

%H Gunnar Brinkmann and Andreas W. M. Dress, <a href="https://doi.org/10.1006/jagm.1996.0806">A constructive enumeration of fullerenes</a>, J. Algorithms 23 (1997), no. 2, 345-358.

%H Gunnar Brinkmann, Jan Goedgebeur, Brendan D. McKay, <a href="http://arxiv.org/abs/1207.7010">The Generation of Fullerenes</a>, arXiv:1207.7010v1 [math.CO], 2012.

%H Gunnar Brinkmann, Andreas Dress, <a href="http://users.cecs.anu.edu.au/~bdm/plantri/">fullgen</a>.

%H Gunnar Brinkmann, Jan Goedgebeur, Brendan D. McKay, <a href="http://caagt.ugent.be/buckygen/">buckygen</a>.

%H CombOS - Combinatorial Object Server, <a href="http://combos.org/fullgen">generate fullerenes</a>

%H House of Graphs, <a href="https://houseofgraphs.org/meta-directory/fullerenes">Fullerenes</a>.

%H A. M. Livshits and Yu. E. Lozovik, <a href="https://doi.org/10.1021/ci0342573">Cut-and-unfold approach to fullerene enumeration</a>, J. Chem. Inf. Comput. Sci., (2004), vol. 44, 1517-1520.

%Y Cf. A086423, A007894, A057210.

%K nonn,nice

%O 30,9

%A _Gunnar Brinkmann_ and A. Dress (dress(AT)mathematik.uni-bielefeld.de)

%E Added a(121)-a(200). a(30)-a(190) is independently confirmed by buckygen and fullgen, while a(191)-a(200) was only computed by buckygen. - _Jan Goedgebeur_, Aug 08 2012