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A268079 T(n,k)=Number of nXk nonnegative integer arrays with new values introduced in each row and column in sequential order starting with zero.

%I A268079 #4 Jan 25 2016 21:23:38
%S A268079 1,1,1,1,2,1,1,4,4,1,1,8,18,8,1,1,16,86,86,16,1,1,32,422,1094,422,32,
%T A268079 1,1,64,2094,15106,15106,2094,64,1,1,128,10438,216734,637358,216734,
%U A268079 10438,128,1,1,256,52126,3168306,29309170,29309170,3168306,52126,256,1,1,512
%N A268079 T(n,k)=Number of nXk nonnegative integer arrays with new values introduced in each row and column in sequential order starting with zero.
%C A268079 Table starts
%C A268079 .1...1......1.........1.............1.................1.....................1
%C A268079 .1...2......4.........8............16................32....................64
%C A268079 .1...4.....18........86...........422..............2094.................10438
%C A268079 .1...8.....86......1094.........15106............216734...............3168306
%C A268079 .1..16....422.....15106........637358..........29309170............1412290158
%C A268079 .1..32...2094....216734......29309170........4617638834..........795460720710
%C A268079 .1..64..10438...3168306....1412290158......795460720710.......517992936833258
%C A268079 .1.128..52126..46777214...69903748498...144635795908942....369867566612849678
%C A268079 .1.256.260502.694585586.3516426536462.27199854725237562.280350778114908738774
%H A268079 R. H. Hardin, <a href="/A268079/b268079.txt">Table of n, a(n) for n = 1..220</a>
%F A268079 Empirical for column k:
%F A268079 k=1: a(n) = a(n-1)
%F A268079 k=2: a(n) = 2*a(n-1)
%F A268079 k=3: a(n) = 7*a(n-1) -10*a(n-2)
%F A268079 k=4: a(n) = 36*a(n-1) -463*a(n-2) +2640*a(n-3) -6700*a(n-4) +6000*a(n-5)
%F A268079 k=5: [order 14]
%F A268079 k=6: [order 45]
%e A268079 Some solutions for n=4 k=4
%e A268079 ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e A268079 ..0..1..0..1....0..0..0..0....0..1..0..1....0..1..1..0....0..0..1..0
%e A268079 ..0..1..1..1....0..1..1..1....0..0..1..2....0..0..1..0....0..0..1..1
%e A268079 ..0..0..1..2....0..1..2..1....0..1..1..0....0..1..0..0....0..0..0..1
%Y A268079 Column 2 is A000079(n-1).
%Y A268079 Column 3 is A082685(n-1).
%K A268079 nonn,tabl
%O A268079 1,5
%A A268079 _R. H. Hardin_, Jan 25 2016