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 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 (list; table; graph; refs; listen; history; text; internal format)
 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 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: A097540 A112327 A152541 * A093114 A016740 A193145 Adjacent sequences:  A302336 A302337 A302338 * A302340 A302341 A302342 KEYWORD nonn,tabl AUTHOR Geoffrey Critzer, Apr 05 2018 STATUS approved

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Last modified May 16 00:49 EDT 2021. Contains 343937 sequences. (Running on oeis4.)