%I #6 Aug 12 2016 06:55:35
%S 1,1,1,1,3,2,1,10,11,6,1,35,91,54,24,1,126,829,924,330,120,1,462,8013,
%T 19696,10924,2430,720,1,1716,80497,456052,499523,147340,20970,5040,1,
%U 6435,830673,11169884,26266875,13895954,2247540,207900,40320,1,24310
%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 northeast neighbor modulo n and the upper left element equal to 0.
%C Table starts
%C ......1........1.........1...........1............1............1..............1
%C ......1........3........10..........35..........126..........462...........1716
%C ......2.......11........91.........829.........8013........80497.........830673
%C ......6.......54.......924.......19696.......456052.....11169884......284749896
%C .....24......330.....10924......499523.....26266875...1478892354....87594047188
%C ....120.....2430....147340....13895954...1578668020.197549600170.26227806728176
%C ....720....20970...2247540...422626232.100947966762
%C ...5040...207900..38338680.14039428460
%C ..40320..2331000.723997540
%C .362880.29189160
%H R. H. Hardin, <a href="/A267836/b267836.txt">Table of n, a(n) for n = 1..72</a>
%e Some solutions for n=4 k=4
%e ..0..1..1..2....0..1..2..3....0..1..3..0....0..3..0..0....0..1..0..2
%e ..2..1..3..0....1..2..0..3....1..0..1..1....0..1..1..3....1..1..3..2
%e ..2..3..1..3....3..1..0..2....0..2..2..3....1..2..3..2....2..3..3..0
%e ..3..2..0..0....2..0..3..1....2..3..3..2....2..3..2..1....3..0..1..2
%Y Column 1 is A000142(n-1).
%Y Row 2 is A001700(n-1).
%Y Row 3 is A266656.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 21 2016