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%I #5 Dec 18 2015 18:18:33
%S 0,0,1,0,1,27,0,1,69,282,0,1,123,1434,2050,0,1,195,4182,20810,12405,0,
%T 1,273,9762,103050,260235,67557,0,1,375,19110,368130,2273505,3037167,
%U 344708,0,1,477,34602,1042030,12775065,47922021,34229076,1686132,0,1,603
%N T(n,k)=Number of idempotent n X n 0..k matrices of rank n-2
%C Table starts
%C .......0........0........0.........0........0.......0.....0...0.0.0
%C .......1........1........1.........1........1.......1.....1...1.1
%C ......27.......69......123.......195......273.....375...477.603
%C .....282.....1434.....4182......9762....19110...34602.56982
%C ....2050....20810...103050....368130..1042030.2563150
%C ...12405...260235..2273505..12775065.52968495
%C ...67557..3037167.47922021.427616679
%C ..344708.34229076
%C .1686132
%H R. H. Hardin, <a href="/A224118/b224118.txt">Table of n, a(n) for n = 1..52</a>
%e Some solutions for n=3 k=4
%e ..1..0..0....1..3..0....1..3..0....0..3..3....0..0..0....0..1..0....0..0..1
%e ..1..0..0....0..0..0....0..0..0....0..1..1....0..0..1....0..1..0....0..0..3
%e ..3..0..0....1..3..0....0..0..0....0..0..0....0..0..1....0..0..0....0..0..1
%Y Row 3 is A224525
%Y Row 4 is A224115
%K nonn,tabl
%O 1,6
%A _R. H. Hardin_ Apr 09 2013
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