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A268056 T(n,k)=Number of nXk 0..2 arrays with new values introduced in each row and column in sequential order starting with zero.

%I A268056 #4 Jan 25 2016 11:01:44
%S A268056 1,1,1,1,2,1,1,4,4,1,1,8,18,8,1,1,16,86,86,16,1,1,32,422,1082,422,32,
%T A268056 1,1,64,2094,14554,14554,2094,64,1,1,128,10438,200818,560778,200818,
%U A268056 10438,128,1,1,256,52126,2796826,22501266,22501266,2796826,52126,256,1,1,512
%N A268056 T(n,k)=Number of nXk 0..2 arrays with new values introduced in each row and column in sequential order starting with zero.
%C A268056 Table starts
%C A268056 .1...1......1.........1.............1................1....................1
%C A268056 .1...2......4.........8............16...............32...................64
%C A268056 .1...4.....18........86...........422.............2094................10438
%C A268056 .1...8.....86......1082.........14554...........200818..............2796826
%C A268056 .1..16....422.....14554........560778.........22501266............915745002
%C A268056 .1..32...2094....200818......22501266.......2666449962.........322124540754
%C A268056 .1..64..10438...2796826.....915745002.....322124540754......116124404018058
%C A268056 .1.128..52126..39082562...37450557314...39169337042938....42209510913723266
%C A268056 .1.256.260502.546791114.1534144563898.4773343640706306.15385058360607977882
%H A268056 R. H. Hardin, <a href="/A268056/b268056.txt">Table of n, a(n) for n = 1..760</a>
%F A268056 Empirical for column k:
%F A268056 k=1: a(n) = a(n-1)
%F A268056 k=2: a(n) = 2*a(n-1)
%F A268056 k=3: a(n) = 7*a(n-1) -10*a(n-2)
%F A268056 k=4: a(n) = 21*a(n-1) -108*a(n-2) +140*a(n-3)
%F A268056 k=5: a(n) = 62*a(n-1) -969*a(n-2) +4568*a(n-3) -5740*a(n-4)
%F A268056 k=6: a(n) = 184*a(n-1) -8533*a(n-2) +122786*a(n-3) -563036*a(n-4) +700280*a(n-5)
%F A268056 k=7: a(n) = 549*a(n-1) -75693*a(n-2) +3237331*a(n-3) -45379926*a(n-4) +206208420*a(n-5) -255602200*a(n-6)
%e A268056 Some solutions for n=4 k=4
%e A268056 ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e A268056 ..0..1..0..0....0..1..1..0....0..0..1..1....0..1..0..0....0..1..1..1
%e A268056 ..0..1..0..0....0..1..1..0....0..1..1..2....0..0..0..0....0..1..1..2
%e A268056 ..0..1..0..1....0..0..0..0....0..1..1..2....0..0..0..1....0..1..1..1
%Y A268056 Column 2 is A000079(n-1).
%Y A268056 Column 3 is A082685(n-1).
%K A268056 nonn,tabl
%O A268056 1,5
%A A268056 _R. H. Hardin_, Jan 25 2016