A348958 Triangular array read by rows. T(n,k) = A002884(n)/A002884(n-k)*2^((n-k)(n-k-1)), n>=0, 0<=k<=n.

1, 1, 1, 4, 6, 6, 64, 112, 168, 168, 4096, 7680, 13440, 20160, 20160, 1048576, 2031616, 3809280, 6666240, 9999360, 9999360, 1073741824, 2113929216, 4095737856, 7679508480, 13439139840, 20158709760, 20158709760, 4398046511104, 8727373545472, 17182016667648, 33290157293568, 62419044925440, 109233328619520, 163849992929280, 163849992929280

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.

Links

Table of n, a(n) for n=0..35.

Formula

T(n,k) = A002884(n)/A002884(n-k)*2^((n-k)(n-k-1)).

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

Cf. A348622, A002884 (main diagonal), A053763 (column k=0).

Sequence in context: A019203 A365084 A082237 * A348348 A042976 A090142

Adjacent sequences: A348955 A348956 A348957 * A348959 A348960 A348961

Keyword

nonn,tabl

Author

Geoffrey Critzer, Nov 04 2021

Status

approved