

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

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


LINKS



FORMULA



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).


KEYWORD

hard,nice,nonn


AUTHOR



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


STATUS

approved



