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).

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

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, n-1))))}
{ 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