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%I #4 Nov 24 2014 20:09:07
%S 50,222,222,867,1180,867,3123,5029,5029,3123,10660,18859,21955,18859,
%T 10660,35064,65310,82023,82023,65310,35064,112373,214812,279161,
%U 300131,279161,214812,112373,353517,682921,896191,993123,993123,896191,682921
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)-x(i-1,j) in the j direction
%C Table starts
%C ......50......222......867......3123.....10660......35064.....112373.....353517
%C .....222.....1180.....5029.....18859.....65310.....214812.....682921....2122743
%C .....867.....5029....21955.....82023....279161.....896191....2771901....8374485
%C ....3123....18859....82023....300131....993123....3088923....9240559...26984403
%C ...10660....65310...279161....993123...3183434....9580060...27710543...78195145
%C ...35064...214812...896191...3088923...9580060...27910024...78204775..213775147
%C ..112373...682921..2771901...9240559..27710543...78204775..212707851..565044857
%C ..353517..2122743..8374485..26984403..78195145..213775147..565044857.1462376991
%C .1097430..6501118.24944039..77707851.217483704..575554760.1478308633.3731976469
%C .3374226.19720580.73714737.222271083.600720730.1537251580.3832617341.9435234815
%H R. H. Hardin, <a href="/A250527/b250527.txt">Table of n, a(n) for n = 1..241</a>
%F Empirical for column k (k=2 recurrence also works for k=1):
%F k=1: a(n) = 9*a(n-1) -31*a(n-2) +51*a(n-3) -40*a(n-4) +12*a(n-5)
%F k=2-7: a(n) = 14*a(n-1) -85*a(n-2) +294*a(n-3) -639*a(n-4) +906*a(n-5) -839*a(n-6) +490*a(n-7) -164*a(n-8) +24*a(n-9)
%e Some solutions for n=3 k=4
%e ..2..2..1..1..0....2..2..1..1..0....2..1..0..0..1....2..2..1..0..0
%e ..2..2..1..1..0....1..1..0..1..0....1..0..0..0..1....1..1..1..0..0
%e ..1..1..1..1..1....0..2..1..2..1....2..1..1..1..2....1..1..2..1..1
%e ..1..2..2..2..2....0..2..1..2..2....1..0..0..0..1....1..1..2..1..1
%Y Column 1 is A222993(n+1)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 24 2014
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