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%I #4 Nov 24 2014 20:53:53
%S 110,700,700,3958,6012,3958,21326,44017,44017,21326,110546,289035,
%T 393910,289035,110546,559824,1767743,3091263,3091263,1767743,559824,
%U 2787971,10248336,21783369,28135982,21783369,10248336,2787971,13727380,57297797
%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with nondecreasing max(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 .......110........700.........3958.........21326.........110546..........559824
%C .......700.......6012........44017........289035........1767743........10248336
%C ......3958......44017.......393910.......3091263.......21783369.......142934266
%C .....21326.....289035......3091263......28135982......226449945......1660642705
%C ....110546....1767743.....21783369.....226449945.....2039109478.....16593620611
%C ....559824...10248336....142934266....1660642705....16593620611....147966207622
%C ...2787971...57297797....885728348...11375090117...124278132580...1206582455860
%C ..13727380..311492811...5269466799...73739279943...875253351485...9161797846382
%C ..67045240.1660155153..30337133947..459022341499..5860027163649..65815657637488
%C .325579124.8712978900.170444570767.2761125746280.37730281398462.451382788443396
%H R. H. Hardin, <a href="/A250536/b250536.txt">Table of n, a(n) for n = 1..238</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 16]
%F k=2: [order 29]
%F k=3: [order 65] for n>66
%e Some solutions for n=2 k=4
%e ..0..0..0..1..2....0..0..0..1..2....0..0..0..1..3....0..0..0..1..3
%e ..0..0..1..1..3....0..0..2..1..3....3..1..1..1..3....3..1..2..2..3
%e ..2..3..0..2..3....1..2..0..2..3....1..3..2..2..3....1..3..1..3..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 24 2014