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%I #4 Dec 19 2013 06:40:12
%S 205808,10268904,11758836,502595832,2080660489,671548560,24576912260,
%T 357463146593,421353160493,38351813588,1199897571228,61295636223137,
%U 253278425289056,85328128508052,2190245258368,58576345841356
%N T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with no increasing sequence of length 3 horizontally or diagonally downwards
%C Table starts
%C ........205808..........10268904.............502595832..............24576912260
%C ......11758836........2080660489..........357463146593...........61295636223137
%C .....671548560......421353160493.......253278425289056.......151699488521954708
%C ...38351813588....85328128508052....179447238884491424....375374879187809108516
%C .2190245258368.17279764673423169.127129186239945486040.928769780045181953374609
%H R. H. Hardin, <a href="/A234068/b234068.txt">Table of n, a(n) for n = 1..111</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 7]
%F k=2: [order 14]
%F k=3: [order 26]
%F Empirical for row n:
%F n=1: [linear recurrence of order 54]
%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..1..0....0..0..1..1..2..0....0..0..1..0..1..1....0..0..0..1..0..1
%e ..2..2..1..1..2..1....2..2..3..1..0..0....1..1..2..1..3..1....1..3..1..1..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 19 2013