A302339 Triangle read by rows: T(n,k) = number of linear operators T on an n-dimensional vector space over GF(2) such that U is invariant under T for some given k-dimensional subspace U.

1, 2, 2, 16, 8, 16, 512, 128, 128, 512, 65536, 8192, 4096, 8192, 65536, 33554432, 2097152, 524288, 524288, 2097152, 33554432, 68719476736, 2147483648, 268435456, 134217728, 268435456, 2147483648, 68719476736

Offset

0,2

Comments

A subspace U is invariant under operator T if T(u) is in U for all u in U.

Main diagonal is A002416(n).

Links

Table of n, a(n) for n=0..27.

Formula

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

Example

         1;
         2,       2;
        16,       8,     16;
       512,     128,    128,    512;
     65536,    8192,   4096,   8192,   65536;
  33554432, 2097152, 524288, 524288, 2097152, 33554432;

Mathematica

Clear[t]; t[n_, k_] := q^(k^2) q^(n (n - k));
Table[Table[t[n, k], {k, 0, n}], {n, 0, 5}] /. q -> 2 // Grid

Prog

(Magma) /* As triangle */ [[2^(k^2)*2^(n*(n-k)): k in [0..n]]: n in [0.. 10]]; // Vincenzo Librandi, Apr 08 2018

Crossrefs

Cf. A302346.

Sequence in context: A345225 A112327 A152541 * A361817 A093114 A016740

Adjacent sequences: A302336 A302337 A302338 * A302340 A302341 A302342

Keyword

nonn,tabl

Author

Geoffrey Critzer, Apr 05 2018

Status

approved