|
|
A328044
|
|
Number of chains of binary matrices of order n.
|
|
10
|
|
|
1, 3, 299, 28349043, 21262618727925419, 426789461753903103302333992563, 576797123806621878513443912437627670334052360619, 110627172261659730424051586605958905845740712964061737226074854597705843
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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^2-th 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^2-th row of triangle A038719.
|
|
LINKS
|
V. Murali and B. Makamba, Finite Fuzzy Sets, International Journal of General Systems, Vol. 34 (1) (2005), pp. 61-75.
|
|
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 n-set), A007047 (chains in power set of an n-set).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|