

A365534


Number of convergent Boolean relation matrices on [n].


8




OFFSET

0,2


COMMENTS

A Boolean relation matrix R is convergent iff R^k = R^(k+1) for all sufficiently large k. In other words, iff the period of R is equal to 1. The digraph of R is such that all its maximal cyclic nets are primitive (A070322) iff R is convergent. Cf. Rosenblatt link. Also, R is convergent iff every diagonal block in its Frobenius normal form is either primitive or a 1 X 1 zero matrix, Theorem 1.1 in Gregory, Kirkland and Pullman.


LINKS



FORMULA

Sum_{n>=0} a_n*x^n/(n!*2^binomial(n,2)) = 1/(E(x) @ exp((p(x)1+x))) where E(x) = Sum_{n>=0} x^n/(n!*2^binomial(n,2)), p(x) = Sum_{n>=0} A070322(n)x^n/n! and @ is the exponential Hadamard product (see Panafieu and Dovgal).


CROSSREFS



KEYWORD

nonn,more


AUTHOR



STATUS

approved



