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%I #4 Nov 25 2014 13:35:13
%S 40,167,167,639,825,639,2375,3641,3641,2375,8625,14983,17718,14983,
%T 8625,30952,59160,79415,79415,59160,30952,110187,226985,333355,379397,
%U 333355,226985,110187,390391,855988,1347397,1686514,1686514,1347397,855988
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with nondecreasing max(x(i,j),x(i,j-1)) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction
%C Table starts
%C ......40......167.......639.......2375.......8625.......30952.......110187
%C .....167......825......3641......14983......59160......226985.......855988
%C .....639.....3641.....17718......79415.....333355.....1347397......5284985
%C ....2375....14983.....79415.....379397....1686514.....7120483.....29029369
%C ....8625....59160....333355....1686514....7838610....34503682....145409040
%C ...30952...226985...1347397....7120483...34503682...157109231....683598422
%C ..110187...855988...5284985...29029369..145409040...683598422...3053953408
%C ..390391..3188758..20355558..115191907..595065843..2872989261..13166219146
%C .1378890.11789698..77281643..448833569.2377121443.11770195566..55124490255
%C .4860979.43358285.290814703.1723204432.9335358862.47219522093.225879886123
%H R. H. Hardin, <a href="/A250592/b250592.txt">Table of n, a(n) for n = 1..385</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 9]
%F k=2: [order 13]
%F k=3: [order 26] for n>27
%F k=4: [order 33] for n>35
%F k=5: [order 49] for n>54
%F k=6: [order 58] for n>64
%F k=7: [order 79] for n>88
%e Some solutions for n=3 k=4
%e ..0..0..0..1..1....0..0..0..0..2....0..0..0..0..0....0..1..1..1..1
%e ..0..0..0..2..2....1..0..0..2..2....0..0..1..0..0....1..0..1..1..2
%e ..0..1..1..2..2....0..1..2..2..2....0..1..0..1..0....0..2..1..1..2
%e ..0..2..2..2..2....1..2..2..2..2....1..0..1..0..2....2..1..2..1..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 25 2014
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