T(n,k) = Number of idempotent n X n 0..k matrices of rank 2.

Terms

a(0) =0a(1) =0a(2) =1a(3) =0a(4) =1a(5) =21a(6) =0a(7) =1a(8) =51a(9) =282a(10) =0a(11) =1a(12) =93a(13) =1434a(14) =3070a(15) =0a(16) =1a(17) =147a(18) =4182a(19) =30410a(20) =29505a(21) =0a(22) =1a(23) =213a(24) =9762a(25) =136990a(26) =546465a(27) =260967a(28) =0a(29) =1