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.

1, 2, 13, 219, 9322, 982243, 249233239, 148346645212, 202688186994599, 624913864623500599, 4289324010827093793808, 64841661094150427710360745, 2140002760057211517052090865983, 153082134018816602622335941790247946, 23590554099141037133024176892280338280237

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

Table of n, a(n) for n=0..14.

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

Cf. A003024, A355612, A365534, A365590, A366141.

Sequence in context: A227746 A078702 A259795 * A069569 A255882 A015196

Adjacent sequences: A365590 A365591 A365592 * A365594 A365595 A365596

Keyword

nonn

Author

Geoffrey Critzer, Sep 10 2023

Status

approved