A139622 Triangle read by rows: T(n,k) is the number of strongly connected directed multigraphs with loops, with n arcs and k vertices.

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, 301, 16, 1, 1, 60, 1215, 6476, 9724, 4364, 575, 20, 1, 1, 85, 2542, 21898, 55707, 45284, 12131, 1042, 25, 1, 1, 110, 4951, 65789, 268329, 365063, 175416, 30090, 1749, 30, 1

Offset

1,5

Links

Andrew Howroyd, Table of n, a(n) for n = 1..820 (rows 1..40)

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  301   16  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.

Prog

(PARI) \\ See PARI link in A350489 for program code.
{ my(A=A139622rows(10)); for(n=1, #A, print(A[n])) } \\ Andrew Howroyd, Jan 14 2022

Crossrefs

Row sums are A139627.

Cf. A136564, A139621, A143841, A350489, A350753.

Sequence in context: A186287 A318393 A340128 * A257895 A186023 A103880

Adjacent sequences: A139619 A139620 A139621 * A139623 A139624 A139625

Keyword

nonn,tabl

Author

Benoit Jubin, May 01 2008

Extensions

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

Terms a(34) and beyond from Andrew Howroyd, Jan 14 2022

Status

approved