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%I
%S 36,154,125,585,654,380,2183,2969,2347,1072,7924,12360,12151,7342,
%T 2856,28456,49310,56232,43185,20743,7307,101308,190213,241742,218680,
%U 134878,53847,18131,358990,720347,994030,1014946,747039,381834,130848,43966
%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 min(x(i,j),x(i-1,j)) in the j direction
%C Table starts
%C .....36.....154......585.....2183......7924......28456......101308.......358990
%C ....125.....654.....2969....12360.....49310.....190213......720347......2690076
%C ....380....2347....12151....56232....241742.....994030.....3951204.....15376595
%C ...1072....7342....43185...218680...1014946....4416061....18465586.....74732823
%C ...2856...20743...134878...747039...3719562...17202711....75537881....319253573
%C ...7307...53847...381834..2290189..12291286...60472234...280151655...1237636447
%C ..18131..130848...994281..6421141..37072806..195029867...955747123...4434468137
%C ..43966..300960..2419996.16675794.103697021..584383121..3044656152..14889326715
%C .104755..662000..5560799.40596068.271291108.1641320797..9115002626..47182771424
%C .246252.1402495.12176364.93379730.669808747.4350649060.25819633391.141867614165
%H R. H. Hardin, <a href="/A250632/b250632.txt">Table of n, a(n) for n = 1..480</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 9]
%F k=2: [order 14]
%F k=3: [order 20]
%F k=4: [order 21] for n>24; also a degree 14 polynomial plus a degree 5 quasipolynomial with period 2
%F k=5: [order 22] for n>29; also a degree 14 polynomial plus a degree 6 quasipolynomial with period 2
%F k=6: [order 25] for n>36; also a degree 16 polynomial plus a degree 7 quasipolynomial with period 2
%F k=7: [order 28] for n>43; also a degree 18 polynomial plus a degree 8 quasipolynomial with period 2
%F Empirical for row n:
%F n=1: [linear recurrence of order 8]
%F n=2: [order 13] for n>16
%F n=3: [order 26] for n>29
%F n=4: [order 33] for n>37
%F n=5: [order 49] for n>54
%F n=6: [order 57] for n>63
%F n=7: [order 79] for n>86
%e Some solutions for n=3 k=4
%e ..0..0..0..0..0....0..0..0..0..2....0..0..1..1..1....0..0..0..0..2
%e ..0..0..0..0..0....0..0..1..1..2....0..1..1..1..2....0..0..0..0..2
%e ..0..0..0..0..1....0..1..1..2..1....0..2..1..2..2....0..1..0..0..2
%e ..0..2..2..1..0....2..0..2..1..2....2..1..2..2..2....2..0..1..2..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 26 2014
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