%I A139625
%S A139625 1,1,1,1,1,1,2,1,6,1,10,1,19,1,28,1,1,44,2,1,60,10,1,85,31,1,110,90,1,
%T A139625 146,222,1,182,520,1,231,1090,1,1,280,2180,2,1,344,4090,11,1
%N A139625 Table read by rows: T(n,k) is the number of strongly connected directed 
               multigraphs with loops and no vertex of degree 0, with n arcs and 
               k vertices, which are transitive (the existence of a path between 
               two points implies the existence of an arc between those two points).
%C A139625 Length of the n^th row: floor(sqrt(n)).
%C A139625 These graphs are reflexive (each vertex has a self-loop), so T(n,k) = 
               sum(A139621(n-k^2,m),m=0..k)
%C A139625 T(n,1) = 1, T(n,2) = A005993(n-4), T(n,3) = A050927(n-9), T(n,4) = A050929(n-16).
%C A139625 Row sums: A139630.
%Y A139625 Cf. A139623, A139624.
%Y A139625 Sequence in context: A166120 A007956 A107754 this_sequence A053785 A060173 
               A059344
%Y A139625 Adjacent sequences: A139622 A139623 A139624 this_sequence A139626 A139627 
               A139628
%K A139625 nonn
%O A139625 1,7
%A A139625 Benoit Jubin (benoit_jubin(AT)yahoo.fr), May 01 2008, Sep 01 2008