%I #25 Nov 27 2022 10:50:00

%S 1,2,11,205,14137,3755249,3916674017,16190352314305,

%T 266479066904477569,17503939768635307654913,

%U 4593798697440979773283368449,4819699338906053452395454422580225,20221058158328101246044232181365184919553

%N Number of convergent n X n matrices over GF(2).

%C A matrix A over a finite field is convergent if A^j=A^(j+1) for some j>=1. Every convergent matrix converges to an idempotent matrix. Every idempotent matrix is convergent to itself. Every nilpotent matrix is convergent to the zero matrix.

%F a(n) = Sum_{k=0..n} A296548(n,k)*A053763(n-k).

%t nn = 12; q = 2;g[n_] := Product[q^n - q^i, {i, 0, n - 1}]; Table[Sum[g[n]/(g[k] g[n - k]) q^((n - k) (n - k - 1)), {k, 0, n}], {n, 0, nn}]

%Y Cf. A296548, A053763, A132186.

%K nonn

%O 0,2

%A _Geoffrey Critzer_, Nov 26 2022