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%I #19 Sep 08 2022 08:46:21
%S 1,2,2,16,8,16,512,128,128,512,65536,8192,4096,8192,65536,33554432,
%T 2097152,524288,524288,2097152,33554432,68719476736,2147483648,
%U 268435456,134217728,268435456,2147483648,68719476736
%N 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.
%C A subspace U is invariant under operator T if T(u) is in U for all u in U.
%C Main diagonal is A002416(n).
%F T(n,k) = 2^(k^2)*2^(n(n-k)).
%e 1;
%e 2, 2;
%e 16, 8, 16;
%e 512, 128, 128, 512;
%e 65536, 8192, 4096, 8192, 65536;
%e 33554432, 2097152, 524288, 524288, 2097152, 33554432;
%t Clear[t]; t[n_, k_] := q^(k^2) q^(n (n - k));
%t Table[Table[t[n, k], {k, 0, n}], {n, 0, 5}] /. q -> 2 // Grid
%o (Magma) /* As triangle */ [[2^(k^2)*2^(n*(n-k)): k in [0..n]]: n in [0.. 10]]; // _Vincenzo Librandi_, Apr 08 2018
%Y Cf. A302346.
%K nonn,tabl
%O 0,2
%A _Geoffrey Critzer_, Apr 05 2018
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