A139622 - OEIS

%I #24 Jan 14 2022 19:45:20

%S 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,

%T 1,44,534,1670,1361,301,16,1,1,60,1215,6476,9724,4364,575,20,1,1,85,

%U 2542,21898,55707,45284,12131,1042,25,1,1,110,4951,65789,268329,365063,175416,30090,1749,30,1

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

%H Andrew Howroyd, <a href="/A139622/b139622.txt">Table of n, a(n) for n = 1..820</a> (rows 1..40)

%H R. J. Mathar, <a href="http://arxiv.org/abs/1709.09000">Statistics on Small Graphs</a>, arXiv:1709.09000 (2017) Table 73.

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

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

%e Triangle begins:

%e     1

%e     1    1

%e     1    2    1

%e     1    6    4    1

%e     1   10   19    6    1

%e     1   19   73   59    9    1

%e     1   28  208  350  138   12    1

%e     1   44  534 1670 1361  301   16  1

%e     ...

%e 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.

%e 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.

%o (PARI) \\ See PARI link in A350489 for program code.

%o { my(A=A139622rows(10)); for(n=1, #A, print(A[n])) } \\ _Andrew Howroyd_, Jan 14 2022

%Y Row sums are A139627.

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

%K nonn,tabl

%O 1,5

%A _Benoit Jubin_, May 01 2008

%E More terms from _R. J. Mathar_, Aug 11 2017

%E Terms a(34) and beyond from _Andrew Howroyd_, Jan 14 2022