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R. H. Hardin, <a href="/A250454/b250454.txt">Table of n, a(n) for n = 1..332</a>

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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 min(x(i,j),x(i-1,j)) in the j direction

44, 217, 217, 1000, 2029, 1000, 4535, 17024, 17024, 4535, 20242, 141857, 258377, 141857, 20242, 89677, 1155519, 3865967, 3865967, 1155519, 89677, 395240, 9376751, 56575618, 104578590, 56575618, 9376751, 395240, 1736779, 75647740, 822755006

1,1

Table starts

.......44.........217...........1000..............4535................20242

......217........2029..........17024............141857..............1155519

.....1000.......17024.........258377...........3865967.............56575618

.....4535......141857........3865967.........104578590...........2750712613

....20242.....1155519.......56575618........2750712613.........130213746897

....89677.....9376751......822755006.......71984404630........6120328131599

...395240....75647740....11894220206.....1868402502223......285429015596551

..1736779...609534839...171683275444....48446319776685....13286357317725708

..7617286..4903892459..2474382329697..1253388924506698...617196231962925214

.33369545.39438538201.35650926095264.32426207385598948.28662266869756914003

Empirical for column k:

k=1: a(n) = 6*a(n-1) -3*a(n-2) -20*a(n-3) +6*a(n-4) +12*a(n-5)

k=2: [order 11]

k=3: [order 25]

k=4: [order 50]

k=5: [order 99]

Some solutions for n=2 k=4

..1..0..1..0..2....0..1..0..2..0....0..1..1..1..1....0..0..1..0..1

..0..0..0..0..1....2..0..0..0..0....1..1..2..1..2....1..0..0..0..2

..2..0..2..2..2....0..0..0..0..2....1..1..1..2..1....0..1..2..1..0

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nonn,tabl

R. H. Hardin, Nov 23 2014

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