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A192517 Table read by antidiagonals: T(n,k) = number of multigraphs with n vertices and k edges, with no loops allowed (n >= 1, k >= 0).

%I A192517 #37 May 14 2018 17:00:47
%S A192517 1,1,0,1,1,0,1,1,1,0,1,1,2,1,0,1,1,3,3,1,0,1,1,3,6,4,1,0,1,1,3,7,11,5,
%T A192517 1,0,1,1,3,8,17,18,7,1,0,1,1,3,8,21,35,32,8,1,0,1,1,3,8,22,52,76,48,
%U A192517 10,1,0,1,1,3,8,23,60,132,149,75,12,1,0
%N A192517 Table read by antidiagonals: T(n,k) = number of multigraphs with n vertices and k edges, with no loops allowed (n >= 1, k >= 0).
%C A192517 Rows converge to sequence A050535, i.e. T(n,k) = A050535(k) for n >= 2k.
%D A192517 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 171.
%H A192517 Andrew Howroyd, <a href="/A192517/b192517.txt">Table of n, a(n) for n = 1..1275</a> (terms 1..78 from Alberto Tacchella computed using <a href="http://users.cecs.anu.edu.au/~bdm/nauty/">nauty 2.4</a>, terms 79..595 from Sean A. Irvine computed using cycle index method of Harary and Palmer).
%H A192517 R. J. Mathar, <a href="http://arxiv.org/abs/1709.09000">Statistics on Small Graphs</a>, arXiv:1709.09000 [math.CO] (2017), Table 69.
%e A192517 Table begins:
%e A192517 [1,0,0,0,0,0,0,0,0,...],
%e A192517 [1,1,1,1,1,1,1,1,1,...],
%e A192517 [1,1,2,3,4,5,7,8,10,...],
%e A192517 [1,1,3,6,11,18,32,48,75,...],
%e A192517 [1,1,3,7,17,35,76,149,291,...],
%e A192517 [1,1,3,8,21,52,132,313,741,...],
%e A192517 [1,1,3,8,22,60,173,471,1303,...],
%e A192517 [1,1,3,8,23,64,197,588,1806,...],
%e A192517 ...
%o A192517 (PARI) \\ See A191646 for G function.
%o A192517 R(n)={Mat(vectorv(n, k, concat([1], G(k, n-1))))}
%o A192517 { my(A=R(10)); for(n=1, #A, for(k=1, #A, print1(A[n,k], ", "));print) } \\ _Andrew Howroyd_, May 14 2018
%Y A192517 Cf. A008406, A191646, A003082 (row 4), A014395 (row 5), A014396 (row 6).
%K A192517 nonn,tabl
%O A192517 1,13
%A A192517 _Alberto Tacchella_, Jul 03 2011