cp's OEIS Frontend

A134818 Number of unlabeled connected loopless multigraphs with n nodes of degree 4 or less and with at most triple edges.

%I A134818 #41 Jun 02 2025 16:24:44
%S A134818 1,3,9,37,146,772,4449,30307,228605,1921464,17652327,176162548,
%T A134818 1893738334,21806975279,267636988052,3486370839295,48029272657002,
%U A134818 697542580286159,10649954607360119,170508064788069346,2856122791685125616,49951625299057923405
%N A134818 Number of unlabeled connected loopless multigraphs with n nodes of degree 4 or less and with at most triple edges.
%C A134818 From _Natan Arie Consigli_, May 29 2017: (Start)
%C A134818 Original name was "Number of hydrocarbon structures that can be drawn (excluding stereoisomers)" but this has been replaced with a mathematical definition which is more consistent with the terms of the sequence and the program.
%C A134818 In chemical terms this counts the following, given n carbon atoms:
%C A134818 - carbon allotropes;
%C A134818 - aliphatic hydrocarbons;
%C A134818 - resonance structures of graphically non-equivalent anti-aromatic and aromatic hydrocarbons.
%C A134818 Some molecules are theoretical and may or may not exist.
%C A134818 (End)
%C A134818 Computed over a period of several years and confirmed using the Molgen program.
%C A134818 Terms for n = 8,9,10 calculated using an exhaustive algorithm and Nauty. The algorithm correctly found the 7 known terms and the known acyclic hydrocarbons (up to n=10, see A002986) were extracted from the results correctly. - Vesa Linja-aho (vesa.linja-aho(AT)tkk.fi), Apr 17 2008
%C A134818 Except for a(2), the same as A289157. The extra graph in A289157 is the 4-regular graph on 2 nodes. - _Andrew Howroyd_, Mar 20 2020
%H A134818 Brendan McKay, <a href="http://users.cecs.anu.edu.au/~bdm/nauty/">Nauty</a>
%H A134818 Molgen, <a href="http://molgen.de/?src=documents/publications">Publications</a>
%F A134818 a(n) = A289157(n) for n > 2. - _Andrew Howroyd_, Mar 20 2020
%e A134818 For n = 2 there are a(2) = 3 structures that can be drawn with 2 carbons (ethane, ethene, and ethyne).
%e A134818 For n = 7 there are a(7) = 4449 structures that can be drawn with 7 carbons.
%o A134818 (nauty) geng -c -D4 ${n} -q | multig -m3 -D4 -u
%Y A134818 Cf. A134819 gives the number of possible structures, broken down by units of unsaturation.
%Y A134818 Cf. A002986 (non-cyclic hydrocarbons).
%Y A134818 Cf. A121941, A289157, A289158, A303033.
%K A134818 hard,nice,nonn
%O A134818 1,2
%A A134818 _David Consiglio, Jr._, Jan 28 2008
%E A134818 a(8)-a(10) from Vesa Linja-aho (vesa.linja-aho(AT)tkk.fi), Apr 17 2008
%E A134818 a(11) from Vesa Linja-aho (vesa.linja-aho(AT)tkk.fi), Apr 24 2008
%E A134818 a(12) sent by _David Consiglio, Jr._, Apr 23 2008
%E A134818 a(12) corrected, a(13) and a(14) added - _David Consiglio, Jr._ Nov 03 2011
%E A134818 a(15)-a(17) computed using nauty by _Sean A. Irvine_, Jan 19 2015
%E A134818 New name from _Natan Arie Consigli_, May 29 2016
%E A134818 a(18)-a(22) from _Andrew Howroyd_, Mar 20 2020