%I #11 Feb 06 2023 12:47:59
%S 0,0,1,0,1,21,0,1,51,282,0,1,93,1434,3070,0,1,147,4182,30410,29505,0,
%T 1,213,9762,136990,546465,260967,0,1,291,19110,467290,3784335,8815317,
%U 2175236,0,1,381,34602,1240310,18925485,94529631
%N T(n,k) = Number of idempotent n X n 0..k matrices of rank 2.
%C Table starts:
%C .......0.......0........0........0.......0.....0...0.0.0
%C .......1.......1........1........1.......1.....1...1.1
%C ......21......51.......93......147.....213...291.381
%C .....282....1434.....4182.....9762...19110.34602
%C ....3070...30410...136990...467290.1240310
%C ...29505..546465..3784335.18925485
%C ..260967.8815317.94529631
%C .2175236
%e Some solutions for n=3, k=4:
%e ..1..0..2....0..1..3....0..0..1....0..0..0....0..0..0....1..0..0....1..3..0
%e ..0..1..3....0..1..0....0..1..0....3..1..0....0..1..0....0..1..1....0..0..0
%e ..0..0..0....0..0..1....0..0..1....3..0..1....4..0..1....0..0..0....0..3..1
%Y Row 3 is A224334.
%K nonn,tabl,more
%O 1,6
%A _R. H. Hardin_, Apr 09 2013