%I #4 Nov 26 2014 22:09:47
%S 100,654,536,3674,4958,2435,19876,37892,30719,10050,102963,253578,
%T 301632,160486,38431,521684,1578385,2492054,2003383,735523,138957,
%U 2597784,9240474,18235293,19962956,11250902,3020711,480846,12791393,52069631
%N T(n,k)=Number of (n+1)X(k+1) 0..3 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 ......100.......654........3674........19876........102963.........521684
%C ......536......4958.......37892.......253578.......1578385........9240474
%C .....2435.....30719......301632......2492054......18235293......122690762
%C ....10050....160486.....2003383.....19962956.....171212264.....1307242006
%C ....38431....735523....11250902....133888216....1325146542....11455263558
%C ...138957...3020711....55337801....770143684....8760011881....85271480338
%C ...480846..11354082...242456834...3888150856...50308117796...550734848033
%C ..1607723..39603227...965170215..17539038598..256524870716..3145868632088
%C ..5230029.129764854..3536263608..71841461103.1177985177929.16145490726264
%C .16642735.403049071.12071431807.270529260362.4941673178715.75408944337595
%H R. H. Hardin, <a href="/A250707/b250707.txt">Table of n, a(n) for n = 1..242</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 16]
%F k=2: [order 30]
%F k=3: [order 43] for n>44
%F k=4: [order 42] for n>47
%F k=5: [order 46] for n>57
%F k=6: [order 48] for n>65
%F k=7: [order 50] for n>73
%F Empirical for row n:
%F n=1: [linear recurrence of order 16]
%F n=2: [order 29] for n>34
%F n=3: [order 65] for n>70
%F n=4: [order 93] for n>100
%e Some solutions for n=2 k=4
%e ..0..0..1..1..2....0..0..1..1..3....0..0..0..1..1....0..0..0..0..0
%e ..1..1..2..2..3....0..0..1..2..2....0..1..0..1..2....0..0..0..0..3
%e ..0..3..2..3..3....0..2..2..2..2....2..0..2..1..2....1..1..3..3..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 26 2014