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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 (list; graph; refs; listen; history; text; internal format)



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 non-equivalent anti-aromatic and aromatic hydrocarbons.

Some molecules are theoretical and may or may not exist.


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 Linja-aho (vesa.linja-aho(AT)tkk.fi), Apr 17 2008

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


Table of n, a(n) for n=1..22.

Brendan McKay, Nauty

Molgen, Publications


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


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.


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


Cf. A134819 gives the number of possible structures, broken down by units of unsaturation.

Cf. A002986 (non-cyclic hydrocarbons).

Cf. A121941, A289157, A289158, A303033.

Sequence in context: A197309 A149021 A149022 * A321737 A002751 A245890

Adjacent sequences:  A134815 A134816 A134817 * A134819 A134820 A134821




David Consiglio, Jr., Jan 28 2008


a(8)-a(10) from Vesa Linja-aho (vesa.linja-aho(AT)tkk.fi), Apr 17 2008

a(11) from Vesa Linja-aho (vesa.linja-aho(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



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Last modified April 14 22:47 EDT 2021. Contains 342971 sequences. (Running on oeis4.)