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T(n,k)=Number of idempotent n X n -k..k matrices of rank 2
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%I #12 Dec 18 2015 18:18:23

%S 0,0,1,0,1,75,0,1,399,4470,0,1,927,90390,224810,0,1,1815,424374

%N T(n,k)=Number of idempotent n X n -k..k matrices of rank 2

%C Table starts

%C ......0.....0......0....0.0.0

%C ......1.....1......1....1.1

%C .....75...399....927.1815

%C ...4470.90390.424374

%C .224810

%e Some solutions for n=3 k=4

%e ..2.-2..2....1..0..0....1..1..0....3..2.-2...-1..3.-2....1..0..0...-1..2..0

%e ..0..1..0...-3..1.-1....0..0..0....1..2.-1...-2..4.-2...-4..1..4...-1..2..0

%e .-1..2.-1...-3..0..0....0..2..1....4..4.-3...-2..3.-1....1..0..0....1.-1..1

%Y Row 3 is A223452

%K nonn,tabl

%O 1,6

%A _R. H. Hardin_ Apr 10 2013