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A358739 Triangular array read by rows. T(n,k) is the number of n X n matrices A over F_2 such that Sum_{phi} nullity(phi(A)) = k where the sum is over all monic irreducible polynomials in F_2[x] that divide the characteristic polynomial of A, n >= 1, 1 <= k <= n.

%I A358739 #11 Dec 15 2022 14:02:24
%S A358739 2,6,10,84,210,218,5040,19740,15330,25426,1249920,5780880,6939660,
%T A358739 7604610,11979362,1259919360,7533267840,9297061200,12276675180,
%U A358739 14280964866,24071588290,5120312279040,34082078607360,48312946523520,78970351980240,88215877158444,112601184828930,195647202043778
%N A358739 Triangular array read by rows.  T(n,k) is the number of n X n matrices A over F_2 such that Sum_{phi} nullity(phi(A)) = k where the sum is over all monic irreducible polynomials in F_2[x] that divide the characteristic polynomial of A, n >= 1, 1 <= k <= n.
%e A358739 Triangle begins
%e A358739         2;
%e A358739         6,      10;
%e A358739        84,     210,     218;
%e A358739      5040,   19740,   15330,   25426;
%e A358739   1249920, 5780880, 6939660, 7604610, 11979362;
%e A358739   ...
%Y A358739 Cf. A346222 (main diagonal), A083402 (1/2 * column 1), A002416 (row sums).
%K A358739 nonn,tabl
%O A358739 1,1
%A A358739 _Geoffrey Critzer_, Nov 29 2022