OFFSET
0,2
COMMENTS
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.
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
LINKS
D. A. Gregory, S. Kirkland, and N. J. Pullman, Power convergent Boolean matrices, Linear Algebra and its Applications, Volume 179, 15 January 1993, Pages 105-117.
FORMULA
E.g.f.: D(exp(x)-1+x) where D(x) is the e.g.f. for A003024.
MATHEMATICA
nn = 12; d[x_] :=Total[Cases[Import["https://oeis.org/A003024/b003024.txt",
"Table"], {_, _}][[All, 2]]*Table[x^(i - 1)/(i - 1)!, {i, 1, 41}]];
Range[0, nn]! CoefficientList[Series[d[Exp[x] - 1 + x], {x, 0, nn}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Sep 10 2023
STATUS
approved