login
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
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).
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: A373997 A112327 A152541 * A361817 A093114 A016740
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Apr 05 2018
STATUS
approved