OFFSET
0,5
COMMENTS
The (q = 2) analog of A008279.
A022166(m,k)*T(n,k) is the number of m X n matrices over F_2 that have rank k.
a(n) is the number of n X n matrices over F_2 in Green's R class containing A where rank(A) = k. - Geoffrey Critzer, Oct 05 2022
LINKS
Geoffrey Critzer, Combinatorics of Vector Spaces over Finite Fields, Master's thesis, Emporia State University, 2018.
Jeremy L. Martin, Lecture Notes on Algebraic Combinatorics, 2010-2023, Example 2.3.6.
Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
Wikipedia, Green's relations.
FORMULA
EXAMPLE
1;
1, 1;
1, 3, 6;
1, 7, 42, 168;
1, 15, 210, 2520, 20160;
1, 31, 930, 26040, 624960, 9999360;
...
MATHEMATICA
Table[Table[Product[q^n - q^i, {i, 0, k - 1}] /. q -> 2, {k, 0, n}], {n, 0, 8}] // Grid
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Jun 18 2017
STATUS
approved