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%I
%S 40,169,158,646,872,612,2359,4007,4111,2323,8298,16993,21955,18387,
%T 8726,28450,67409,104674,111175,80133,32554,95628,255502,456514,
%U 590305,542834,344135,120930,316568,934786,1869400,2800667,3184615,2592734,1466191
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction
%C Table starts
%C ......40.......169........646........2359........8298........28450
%C .....158.......872.......4007.......16993.......67409.......255502
%C .....612......4111......21955......104674......456514......1869400
%C ....2323.....18387.....111175......590305.....2800667.....12340547
%C ....8726.....80133.....542834.....3184615....16381510.....77449279
%C ...32554....344135....2592734....16694358....92713991....469255626
%C ..120930...1466191...12238954....86049801...514669302...2783159034
%C ..447985...6219851...57388086...438901153..2820364768..16265322280
%C .1656600..26329263..268220043..2225675881.15340901571..94211007762
%C .6118822.111352239.1251995646.11253642389.83091814176.542676800586
%H R. H. Hardin, <a href="/A250994/b250994.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = 6*a(n-1) -7*a(n-2) -8*a(n-3) +7*a(n-4) +6*a(n-5) +a(n-6)
%F k=2: [order 12]
%F k=3: [order 20]
%F k=4: [order 33]
%F k=5: [order 51]
%F k=6: [order 78]
%F Empirical for row n:
%F n=1: a(n) = 6*a(n-1) -7*a(n-2) -12*a(n-3) +15*a(n-4) +11*a(n-5) -5*a(n-6) -3*a(n-7)
%F n=2: [order 14]
%F n=3: [order 23]
%F n=4: [order 34]
%F n=5: [order 43] for n>45
%F n=6: [order 54] for n>58
%F n=7: [order 67] for n>73
%e Some solutions for n=3 k=4
%e ..1..2..0..2..0....0..0..1..0..2....1..0..0..0..1....0..1..0..2..0
%e ..1..2..0..2..0....0..1..0..1..0....1..0..0..1..0....1..0..1..0..2
%e ..1..2..0..1..2....0..2..1..0..2....1..1..1..2..1....1..0..1..0..2
%e ..1..2..0..1..1....1..1..2..1..0....1..1..2..1..2....1..0..1..2..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 29 2014
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