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A139622 Triangle read by rows: T(n,k) is the number of strongly connected directed multigraphs with loops, with n arcs and k vertices. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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.
Sequence in context: A186287 A318393 A340128 * A257895 A186023 A103880
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

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)