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%I #4 Nov 28 2014 19:03:22
%S 37,155,125,599,699,413,2247,3355,2812,1333,8189,15431,16208,10528,
%T 4213,29281,67595,87529,71014,37477,13111,103093,287045,442409,444421,
%U 289407,128507,40357,358683,1188599,2130148,2572787,2067987,1115035,428095
%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 absolute value of x(i,j)-x(i-1,j) in the j direction
%C Table starts
%C ......37......155.......599.......2247........8189........29281........103093
%C .....125......699......3355......15431.......67595.......287045.......1188599
%C .....413.....2812.....16208......87529......442409......2130148.......9865706
%C ....1333....10528.....71014.....444421.....2572787.....14019652......72722706
%C ....4213....37477....289407....2067987....13550488.....82716842.....475951361
%C ...13111...128507...1115035....8976385....65910564....447407616....2839711239
%C ...40357...428095...4106983...36809498...300230097...2251710502...15686582837
%C ..123271..1394237..14585505..144007880..1294549437..10665462156...81197881457
%C ..374509..4460779..50276307..541598982..5327479262..47958734697..397409857238
%C .1133503.14073313.169096201.1969991292.21062394646.206139574253.1852256126330
%H R. H. Hardin, <a href="/A250942/b250942.txt">Table of n, a(n) for n = 1..144</a>
%F Empirical for column k:
%F k=1: a(n) = 8*a(n-1) -23*a(n-2) +28*a(n-3) -12*a(n-4) for n>6
%F k=2: [order 7] for n>11
%F k=3: [order 15] for n>21
%F k=4: [order 21] for n>29
%F k=5: [order 27] for n>37
%F k=6: [order 33] for n>45
%F k=7: [order 39] for n>53
%F Empirical for row n:
%F n=1: a(n) = 6*a(n-1) -6*a(n-2) -15*a(n-3) +14*a(n-4) +12*a(n-5)
%F n=2: [order 11]
%F n=3: [order 21]
%F n=4: [order 38]
%F n=5: [order 60]
%F n=6: [order 88]
%e Some solutions for n=3 k=4
%e ..2..1..0..0..2....0..0..1..1..1....1..2..0..0..2....2..0..0..1..0
%e ..2..1..0..0..2....0..0..1..2..0....2..1..1..1..1....2..0..0..1..0
%e ..2..1..0..1..1....0..0..1..2..0....2..1..2..2..0....2..0..0..2..2
%e ..2..1..0..1..2....1..1..2..1..1....2..1..2..2..0....2..0..0..2..2
%Y Column 1 is A250891
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 28 2014
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