

A328044


Number of chains of binary matrices of order n.


10



1, 3, 299, 28349043, 21262618727925419, 426789461753903103302333992563, 576797123806621878513443912437627670334052360619, 110627172261659730424051586605958905845740712964061737226074854597705843
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OFFSET

0,2


COMMENTS

For n >= 1, a(n) is the number of chains of n X n (0, 1) matrices.
a(n) is also the number of chains in the power set of n^2 elements.
a(n) is the n^2th term of A007047.
A chain of binary (crisp or Boolean or logical) matrices of order n can be thought of as a fuzzy matrix of order n.
a(n) is the number of distinct n X n fuzzy matrices.
a(n) is the sum of the n^2th row of triangle A038719.


LINKS

V. Murali and B. Makamba, Finite Fuzzy Sets, International Journal of General Systems, Vol. 34 (1) (2005), pp. 6175.


FORMULA

Let T(n, k) denote the number of chains of binary matrices of order n of length k, T(0, 0) = 1, T(0, k) = 0 for k > 0, thus T(n, k) = A038719(n, k).
a(n) = Sum_{k=0..n^2} T(n, k); a(0) = 1.


MAPLE

# P are the polynomials defined in A007047.
A328044 := n > 2^(n^2)*subs(x=1/2, P(n^2, x)):


MATHEMATICA

Table[2*PolyLog[n^2, 1/2]  1 , {n, 0, 29}]


CROSSREFS

Cf. A000079 (subsets of an nset), A007047 (chains in power set of an nset).


KEYWORD

nonn


AUTHOR



STATUS

approved



