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A139622 Table read by rows: T(n,k) is the number of strongly connected directed multigraphs with loops, with n arcs and k vertices. 3
1, 1, 1, 1, 2, 1, 1, 6, 4, 1, 1, 10, 19, 6, 1, 1, 19, 73, 59, 9, 1, 1, 28, 208, 350, 138, 12, 1, 1, 44, 534, 1670, 1361 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..33.

R. J. Mathar, Statistics on Small Graphs, arXiv:1709.09000 (2017) Table 73.

FORMULA

T(n,1) = T(n,n) = 1.

T(n,2) = A139621(n,2) - n(n+1)/2.

EXAMPLE

Triangle begins:

    1

    1    1

    1    2    1

    1    6    4    1

    1   10   19    6    1

    1   19   73   59    9    1

    1   28  208  350  138   12    1

    1   44  534 1670 1361    .    .    1

T(4 edges, 2 vertices)=6: one graph 1->1, 1->1, 2->1, 1->2; one graph 1->1, 2->1, 2->1, 1->2; one graph 1->1, 1->2, 1->2, 2->1; one graph 1->1, 1->2, 2->1, 2->2; one graph 2->1, 2->1, 2->1, 1->2; one graph 1->2, 1->2, 2->1, 2->1.

T(4 edges, 3 vertices)=4: one graph 1->1, 2->1, 3->2, 1->3; one graph 2->1, 2->1, 3->2, 1->3; one graph 2->1, 3->1, 1->2, 1->3; one graph 2->1, 3->1, 1->2, 2->3.

CROSSREFS

Cf. A136564, A139621, A139627 (row sums).

Sequence in context: A158389 A186287 A318393 * A257895 A186023 A103880

Adjacent sequences:  A139619 A139620 A139621 * A139623 A139624 A139625

KEYWORD

nonn,tabl,more

AUTHOR

Benoit Jubin, May 01 2008

EXTENSIONS

More terms from R. J. Mathar, Aug 11 2017

STATUS

approved

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Last modified August 10 11:52 EDT 2020. Contains 336379 sequences. (Running on oeis4.)