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%I #38 Mar 20 2020 12:58:39
%S 1,3,9,37,146,772,4449,30307,228605,1921464,17652327,176162548,
%T 1893738334,21806975279,267636988052,3486370839295,48029272657002,
%U 697542580286159,10649954607360119,170508064788069346,2856122791685125616,49951625299057923405
%N Number of unlabeled connected loopless multigraphs with n nodes of degree 4 or less and with at most triple edges.
%C From _Natan Arie Consigli_, May 29 2017: (Start)
%C 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 In chemical terms this counts the following, given n carbon atoms:
%C - carbon allotropes;
%C - aliphatic hydrocarbons;
%C - resonance structures of graphically non-equivalent anti-aromatic and aromatic hydrocarbons.
%C Some molecules are theoretical and may or may not exist.
%C (End)
%C Computed over a period of several years and confirmed using the Molgen program.
%C 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 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 Brendan McKay, <a href="http://users.cecs.anu.edu.au/~bdm/nauty/">Nauty</a>
%H Molgen, <a href="http://molgen.de/?src=documents/publications">Publications</a>
%F a(n) = A289157(n) for n > 2. - _Andrew Howroyd_, Mar 20 2020
%e For n = 2 there are a(2) = 3 structures that can be drawn with 2 carbons (ethane, ethene, and ethyne).
%e For n = 7 there are a(7) = 4449 structures that can be drawn with 7 carbons.
%o (nauty/bash) geng -c -D4 ${n} -q | multig -m3 -D4 -u
%Y Cf. A134819 gives the number of possible structures, broken down by units of unsaturation.
%Y Cf. A002986 (non-cyclic hydrocarbons).
%Y Cf. A121941, A289157, A289158, A303033.
%K hard,nice,nonn
%O 1,2
%A _David Consiglio, Jr._, Jan 28 2008
%E a(8)-a(10) from Vesa Linja-aho (vesa.linja-aho(AT)tkk.fi), Apr 17 2008
%E a(11) from Vesa Linja-aho (vesa.linja-aho(AT)tkk.fi), Apr 24 2008
%E a(12) sent by _David Consiglio, Jr._, Apr 23 2008
%E a(12) corrected, a(13) and a(14) added - _David Consiglio, Jr._ Nov 03 2011
%E a(15)-a(17) computed using nauty by _Sean A. Irvine_, Jan 19 2015
%E New name from _Natan Arie Consigli_, May 29 2016
%E a(18)-a(22) from _Andrew Howroyd_, Mar 20 2020
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