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T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with every element equal to or 1 greater than any west or northeast neighbors modulo n and the upper left element equal to 0.
11

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

%S 1,1,1,1,3,2,1,10,4,6,1,35,17,5,24,1,126,57,26,6,120,1,462,207,123,45,

%T 7,720,1,1716,786,633,249,82,8,5040,1,6435,3057,3428,1811,502,157,9,

%U 40320,1,24310,12168,18899,14138,4997,1008,306,10,362880,1,92378,49161,106599

%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 west or northeast 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

%C ......1..3...10...35....126......462......1716......6435......24310......92378

%C ......2..4...17...57....207......786......3057.....12168......49161.....200973

%C ......6..5...26..123....633.....3428.....18899....106599.....618585....3674665

%C .....24..6...45..249...1811....14138....114323....938590....7847855...67070467

%C ....120..7...82..502...4997....55105....649089...7866419...97477205.1225988750

%C ....720..8..157.1008..13856...211044...3562990..62745587.1149981951

%C ...5040..9..306.2020..38736...807164..19473397.491779927

%C ..40320.10..605.4044.109231..3087973.106720862

%C .362880.11.1202.8092.310419.11817336

%H R. H. Hardin, <a href="/A267742/b267742.txt">Table of n, a(n) for n = 1..126</a>

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A000142(n-1).

%Y Column 2 is A000027(n+1).

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

%Y Row 3 is A266868.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 20 2016