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%I #4 Dec 16 2013 17:51:58
%S 201664,9828513,11305216,480071296,1909001345,633584640,23453646656,
%T 326595297792,370375897185,35508588544,1144779904896,55891166269184,
%U 220722832237568,71859538054209,1990039158784,55884483506105
%N T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with no increasing sequence of length 3 horizontally or antidiagonally downwards
%C Table starts
%C ........201664...........9828513.............480071296..............23453646656
%C ......11305216........1909001345..........326595297792...........55891166269184
%C .....633584640......370375897185.......220722832237568.......131619893152104448
%C ...35508588544....71859538054209....149185819914631168....309991751661980537856
%C .1990039158784.13941925875538977.100827647839987847168.729964339940515853733888
%H R. H. Hardin, <a href="/A233845/b233845.txt">Table of n, a(n) for n = 1..176</a>
%F Empirical for column k:
%F k=1: a(n) = 56*a(n-1) +16*a(n-2) -768*a(n-3) +512*a(n-4)
%F k=2: [order 12]
%F k=3: [order 16]
%F k=4: [order 32]
%F Empirical for row n:
%F n=1: [linear recurrence of order 56] for n>58
%e Some solutions for n=1 k=4
%e ..0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0
%e ..0..0..0..0..0..3....0..1..1..0..0..0....1..1..0..0..0..0....1..0..0..0..0..3
%e ..3..3..0..0..3..1....0..1..0..0..2..1....1..1..1..1..0..3....0..3..1..1..1..3
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 16 2013