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.

2, 6, 10, 84, 210, 218, 5040, 19740, 15330, 25426, 1249920, 5780880, 6939660, 7604610, 11979362, 1259919360, 7533267840, 9297061200, 12276675180, 14280964866, 24071588290, 5120312279040, 34082078607360, 48312946523520, 78970351980240, 88215877158444, 112601184828930, 195647202043778

Offset

1,1

Links

Table of n, a(n) for n=1..28.

Example

Triangle begins
        2;
        6,      10;
       84,     210,     218;
     5040,   19740,   15330,   25426;
  1249920, 5780880, 6939660, 7604610, 11979362;
  ...

Crossrefs

Cf. A346222 (main diagonal), A083402 (1/2 * column 1), A002416 (row sums).

Sequence in context: A080397 A322756 A048782 * A083458 A124621 A325237

Adjacent sequences: A358736 A358737 A358738 * A358740 A358741 A358742

Keyword

nonn,tabl

Author

Geoffrey Critzer, Nov 29 2022

Status

approved