%I #6 Aug 12 2016 06:55:35

%S 1,1,1,1,3,1,1,10,2,1,1,35,8,2,1,1,126,30,5,2,1,1,462,114,25,5,2,1,1,

%T 1716,414,182,15,5,2,1,1,6435,1561,1256,111,15,5,2,1,1,24310,6227,

%U 7396,1687,67,15,5,2,1,1,92378,25712,39891,23522,761,67,15,5,2,1,1,352716

%N T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with every element equal to or 1 greater than any north or west neighbors modulo n and the upper left element equal to 0.

%C Table starts

%C .1.1..1..1...1....1.....1......1........1..........1............1.............1

%C .1.3.10.35.126..462..1716...6435....24310......92378.......352716.......1352078

%C .1.2..8.30.114..414..1561...6227....25712.....107071.......445688.......1860037

%C .1.2..5.25.182.1256..7396..39891...210384....1168317......7080023......45942141

%C .1.2..5.15.111.1687.23522.253472..2290853...18470974....140294987....1065068657

%C .1.2..5.15..67..761.24745.726627.15303976..251565608...3466082679...42227611356

%C .1.2..5.15..67..457..9204.586844.36708187.1582675968..49970797654.1250823466190

%C .1.2..5.15..67..457..5628.194567.22971957.3039274773.276165720476

%C .1.2..5.15..67..457..5628.119908..7088277

%C .1.2..5.15..67..457..5628.119908

%H R. H. Hardin, <a href="/A268115/b268115.txt">Table of n, a(n) for n = 1..161</a>

%e Some solutions for n=6 k=4

%e ..0..1..1..1....0..0..1..2....0..0..1..1....0..1..2..2....0..0..1..1

%e ..1..2..2..2....1..1..2..3....1..1..2..2....1..2..3..3....0..1..2..2

%e ..2..3..3..3....1..2..3..4....2..2..3..3....2..3..4..4....1..2..3..3

%e ..3..4..4..4....2..3..4..5....3..3..4..4....3..4..5..5....2..3..4..4

%e ..4..5..5..5....3..4..5..0....4..4..5..5....4..5..0..0....3..4..5..5

%e ..5..0..0..0....4..5..5..0....5..5..0..0....5..0..1..1....4..5..5..0

%Y Row 2 is A001700(n-1).

%Y Row 3 is A266319.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 26 2016