

A134818


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


6



1, 3, 9, 37, 146, 772, 4449, 30307, 228605, 1921464, 17652327, 176162548, 1893738334, 21806975279, 267636988052, 3486370839295, 48029272657002, 697542580286159, 10649954607360119, 170508064788069346, 2856122791685125616, 49951625299057923405
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OFFSET

1,2


COMMENTS

From Natan Arie Consigli, May 29 2017: (Start)
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.
In chemical terms this counts the following, given n carbon atoms:
 carbon allotropes;
 aliphatic hydrocarbons;
 resonance structures of graphically nonequivalent antiaromatic and aromatic hydrocarbons.
Some molecules are theoretical and may or may not exist.
(End)
Computed over a period of several years and confirmed using the Molgen program.
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 Linjaaho (vesa.linjaaho(AT)tkk.fi), Apr 17 2008
Except for a(2), the same as A289157. The extra graph in A289157 is the 4regular graph on 2 nodes.  Andrew Howroyd, Mar 20 2020


LINKS

Table of n, a(n) for n=1..22.
Brendan McKay, Nauty
Molgen, Publications


FORMULA

a(n) = A289157(n) for n > 2.  Andrew Howroyd, Mar 20 2020


EXAMPLE

For n = 2 there are a(2) = 3 structures that can be drawn with 2 carbons (ethane, ethene, and ethyne).
For n = 7 there are a(7) = 4449 structures that can be drawn with 7 carbons.


PROG

(nauty/bash) geng c D4 ${n} q  multig m3 D4 u


CROSSREFS

Cf. A134819 gives the number of possible structures, broken down by units of unsaturation.
Cf. A002986 (noncyclic hydrocarbons).
Cf. A121941, A289157, A289158, A303033.
Sequence in context: A197309 A149021 A149022 * A321737 A002751 A245890
Adjacent sequences: A134815 A134816 A134817 * A134819 A134820 A134821


KEYWORD

hard,nice,nonn


AUTHOR

David Consiglio, Jr., Jan 28 2008


EXTENSIONS

a(8)a(10) from Vesa Linjaaho (vesa.linjaaho(AT)tkk.fi), Apr 17 2008
a(11) from Vesa Linjaaho (vesa.linjaaho(AT)tkk.fi), Apr 24 2008
a(12) sent by David Consiglio, Jr., Apr 23 2008
a(12) corrected, a(13) and a(14) added  David Consiglio, Jr. Nov 03 2011
a(15)a(17) computed using nauty by Sean A. Irvine, Jan 19 2015
New name from Natan Arie Consigli, May 29 2016
a(18)a(22) from Andrew Howroyd, Mar 20 2020


STATUS

approved



