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Number of unlabeled graphs with n nodes and an odd number of edges.
8

%I #20 Aug 15 2019 17:01:35

%S 0,1,2,5,16,78,522,6168,137316,6002584,509498932,82545585936,

%T 25251015681176,14527077828617744,15713242984902154384,

%U 32000507852263778595584,122967932076766466336249888,893788862572805850273939095424,12318904626562502262191503745716384

%N Number of unlabeled graphs with n nodes and an odd number of edges.

%H Andrew Howroyd, <a href="/A054960/b054960.txt">Table of n, a(n) for n = 1..50</a>

%H V. A. Liskovets, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/LISK/Derseq.html">Some easily derivable sequences</a>, J. Integer Sequences, 3 (2000), #00.2.2.

%F a(n) = (A000088(n) - A000171(n))/2.

%t Table[Total[Table[NumberOfGraphs[n,m],{m,1,Binomial[n,2],2}]],{n,1,15}] (* _Geoffrey Critzer_, Oct 20 2012 *)

%Y Cf. A000088, A000171.

%Y Cf. A007869 for graphs with an even number of edges.

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_, May 24 2000

%E More terms from _Vladeta Jovovic_, Jul 19 2000

%E Terms a(18) and beyond from _Andrew Howroyd_, Sep 17 2018