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A365593 Number of n X n Boolean relation matrices such that every block of its Frobenius normal form is either a 0 block or a 1 block.

%I A365593 #22 Sep 30 2023 21:46:16
%S A365593 1,2,13,219,9322,982243,249233239,148346645212,202688186994599,
%T A365593 624913864623500599,4289324010827093793808,64841661094150427710360745,
%U A365593 2140002760057211517052090865983,153082134018816602622335941790247946,23590554099141037133024176892280338280237
%N A365593 Number of n X n Boolean relation matrices such that every block of its Frobenius normal form is either a 0 block or a 1 block.
%C A365593 A 1(0) block is such that every entry in the block is 1(0). If a Boolean relation matrix R is limit dominating then it must be that every block of R is either a 0 block or a 1 block.  See Theorem 1.2 in Gregory, Kirkland, and Pullman.
%C A365593 Conjecture: lim_n->inf a(n)/(A003024(n)*2^n) = 1.  In other words, almost all of the relations counted by this sequence have n strongly connected components. - _Geoffrey Critzer_, Sep 30 2023
%H A365593 D. A. Gregory, S. Kirkland, and N. J. Pullman, <a href="https://doi.org/10.1016/0024-3795(93)90323-G">Power convergent Boolean matrices</a>, Linear Algebra and its Applications, Volume 179, 15 January 1993, Pages 105-117.
%F A365593 E.g.f.: D(exp(x)-1+x) where D(x) is the e.g.f. for A003024.
%t A365593 nn = 12; d[x_] :=Total[Cases[Import["https://oeis.org/A003024/b003024.txt",
%t A365593       "Table"], {_, _}][[All, 2]]*Table[x^(i - 1)/(i - 1)!, {i, 1, 41}]];
%t A365593 Range[0, nn]! CoefficientList[Series[d[Exp[x] - 1 + x], {x, 0, nn}],x]
%Y A365593 Cf. A003024, A355612, A365534, A365590, A366141.
%K A365593 nonn
%O A365593 0,2
%A A365593 _Geoffrey Critzer_, Sep 10 2023