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Number of simple connected graphs on n nodes that are not trees.
5

%I #30 Jul 04 2024 09:13:18

%S 0,0,1,4,18,106,842,11094,261033,11716465,1006700330,164059829925,

%T 50335907867918,29003487462844902,31397381142761234219,

%U 63969560113225176156957,245871831682084026519479939,1787331725248899088890200452713,24636021429399867655322650759363689

%N Number of simple connected graphs on n nodes that are not trees.

%H Chai Wah Wu, <a href="/A241841/b241841.txt">Table of n, a(n) for n = 1..87</a> (terms 1..40 from Georg Fischer)

%H Travis Hoppe and Anna Petrone, <a href="https://github.com/thoppe/Encyclopedia-of-Finite-Graphs">Encyclopedia of Finite Graphs</a>

%H T. Hoppe and A. Petrone, <a href="http://arxiv.org/abs/1408.3644">Integer sequence discovery from small graphs</a>, arXiv preprint arXiv:1408.3644 [math.CO], 2014.

%H T. Hoppe and A. Petrone, <a href="http://doi.org/10.1016/j.dam.2015.07.017">Integer sequence discovery from small graphs</a>, Discr. Appl. Math. 201 (2016) 172-181.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CyclicGraph.html">Cyclic Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Tree.html">Tree</a>

%F a(n) = A001349(n) - A000055(n).

%Y Cf. A000055, A001349, A286743, A306003.

%K nonn

%O 1,4

%A _Travis Hoppe_ and _Anna Petrone_, Apr 29 2014