OFFSET
0,4
COMMENTS
Let ~ be the equivalence relation on the set of n X n matrices over GF(2) defined by A ~ B if and only if the dimension of the image of A^n is equal to the dimension of the image of B^n. Let A be a recurrent matrix (Cf A348622) of rank k. Then T(n,k) is the size of the equivalence class containing A.
EXAMPLE
Triangle begins:
1,
1, 1,
4, 6, 6,
64, 112, 168, 168,
4096, 7680, 13440, 20160, 20160,
1048576, 2031616, 3809280, 6666240, 9999360, 9999360
MATHEMATICA
R[n_, d_] := Product[q^n - q^i, {i, 0, n - 1}]/Product[q^(n - d) - q^i, {i, 0, n - d - 1}]; Table[Table[R[n, d] q^((n - d) (n - d - 1)), {d, 0, n}], {n, 0, 10}] // Grid
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Nov 04 2021
STATUS
approved