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%I #4 Nov 25 2014 11:19:44
%S 10,24,24,55,60,55,125,142,142,125,282,329,336,329,282,635,758,778,
%T 778,758,635,1428,1743,1779,1776,1779,1743,1428,3210,4009,4077,4013,
%U 4013,4077,4009,3210,7214,9223,9346,9055,8914,9055,9346,9223,7214,16211,21227
%N T(n,k)=Number of (n+1)X(k+1) 0..1 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 ....10....24.....55....125....282.....635....1428....3210....7214....16211
%C ....24....60....142....329....758....1743....4009....9223...21227....48864
%C ....55...142....336....778...1779....4077....9346...21510...49579...114548
%C ...125...329....778...1776...4013....9055...20510...46664..106695...244907
%C ...282...758...1779...4013...8914...19806...44104...98902..222987...506145
%C ...635..1743...4077...9055..19806...43202...94623..208525..463050..1035676
%C ..1428..4009...9346..20510..44104...94623..203560..441215..963419..2122436
%C ..3210..9223..21510..46664..98902..208525..441215..939730.2019008..4376149
%C ..7214.21227..49579.106695.222987..463050..963419.2019008.4266332..9103961
%C .16211.48864.114548.244907.506145.1035676.2122436.4376149.9103961.19120668
%H R. H. Hardin, <a href="/A250583/b250583.txt">Table of n, a(n) for n = 1..1011</a>
%F Empirical for column k:
%F k=1: a(n) = 3*a(n-1) -a(n-2) -2*a(n-3) +a(n-4)
%F k=2: a(n) = 4*a(n-1) -3*a(n-2) -5*a(n-3) +8*a(n-4) -3*a(n-5)
%F k=3: a(n) = 5*a(n-1) -6*a(n-2) -7*a(n-3) +21*a(n-4) -14*a(n-5) -a(n-6) +4*a(n-7) -a(n-8)
%F k=4: [order 9] for n>10
%F k=5: [order 12] for n>14
%F k=6: [order 12] for n>15
%F k=7: [order 15] for n>19
%e Some solutions for n=6 k=4
%e ..0..0..0..0..1....0..0..0..1..1....0..0..0..0..0....0..0..0..0..0
%e ..0..0..0..0..1....1..1..1..1..1....0..0..0..0..0....0..0..0..1..1
%e ..1..0..0..0..1....0..1..1..1..1....0..0..0..0..0....0..0..1..0..1
%e ..0..1..0..0..1....1..1..1..1..1....0..0..0..0..0....0..1..0..1..0
%e ..1..0..1..1..1....1..1..1..1..1....0..0..1..1..1....1..0..1..0..1
%e ..0..1..1..1..1....0..1..1..1..1....0..0..1..1..1....0..1..0..1..0
%e ..1..0..1..1..1....0..1..1..1..1....0..0..1..1..1....1..0..1..0..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 25 2014
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