

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).


6



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, 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, 10, 1, 0, 1, 1, 3, 8, 23, 60, 132, 149, 75, 12, 1, 0
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OFFSET

1,13


COMMENTS

Rows converge to sequence A050535, i.e. T(n,k) = A050535(k) for n >= 2k.


REFERENCES

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 171.


LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (terms 1..78 from Alberto Tacchella computed using nauty 2.4, terms 79..595 from Sean A. Irvine computed using cycle index method of Harary and Palmer).
R. J. Mathar, Statistics on Small Graphs, arXiv:1709.09000 [math.CO] (2017), Table 69.


EXAMPLE

Table begins:
[1,0,0,0,0,0,0,0,0,...],
[1,1,1,1,1,1,1,1,1,...],
[1,1,2,3,4,5,7,8,10,...],
[1,1,3,6,11,18,32,48,75,...],
[1,1,3,7,17,35,76,149,291,...],
[1,1,3,8,21,52,132,313,741,...],
[1,1,3,8,22,60,173,471,1303,...],
[1,1,3,8,23,64,197,588,1806,...],
...


PROG

(PARI) \\ See A191646 for G function.
R(n)={Mat(vectorv(n, k, concat([1], G(k, n1))))}
{ my(A=R(10)); for(n=1, #A, for(k=1, #A, print1(A[n, k], ", ")); print) } \\ Andrew Howroyd, May 14 2018


CROSSREFS

Cf. A008406, A191646, A003082 (row 4), A014395 (row 5), A014396 (row 6).
Sequence in context: A133607 A103631 A263191 * A309896 A083856 A081718
Adjacent sequences: A192514 A192515 A192516 * A192518 A192519 A192520


KEYWORD

nonn,tabl


AUTHOR

Alberto Tacchella, Jul 03 2011


STATUS

approved



