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A265580 Number of (unlabeled) loopless multigraphs with no isolated vertices such that the sum of the numbers of vertices and edges is n. 3

%I

%S 1,0,0,1,1,2,4,7,13,27,54,112,243,538,1223,2875,6909,17052,43138,

%T 111686,295658,799684,2207356,6213391,17820961,52042771,154640528,

%U 467254731,1434837672,4475520062,14173115724,45548395180,148485883443,490831193397,1644581336531

%N Number of (unlabeled) loopless multigraphs with no isolated vertices such that the sum of the numbers of vertices and edges is n.

%C Also the number of skeletal 2-cliquish graphs with n vertices and no isolated vertices. See Einstein et al. link below.

%H Andrew Howroyd, <a href="/A265580/b265580.txt">Table of n, a(n) for n = 0..100</a>

%H D. Einstein, M. Farber, E. Gunawan, M. Joseph, M. Macauley, J. Propp and S. Rubinstein-Salzedo, <a href="https://arxiv.org/abs/1510.06362">Noncrossing partitions, toggles, and homomesies</a>, arXiv:1510.06362 [math.CO], 2015.

%F a(n) = A265581(n) - A265581(n-1), n>=1.

%e For n = 5, the a(5) = 2 such multigraphs are the graph with three vertices and edges from one vertex to each of the other two, and the graph with two vertices connected by three edges.

%Y Cf. A265581.

%K nonn

%O 0,6

%A _Michael Joseph_, Dec 10 2015

%E Terms a(19) and beyond from _Andrew Howroyd_, Feb 01 2020

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Last modified August 17 12:30 EDT 2022. Contains 356189 sequences. (Running on oeis4.)