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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, northeast or northwest neighbors modulo n and the upper left element equal to 0.
5

%I #7 Aug 12 2016 06:55:35

%S 1,1,1,1,3,2,1,10,2,6,1,35,2,1,24,1,126,2,1,1,120,1,462,2,1,1,1,720,1,

%T 1716,5,1,1,1,1,5040,1,6435,14,1,1,1,1,1,40320,1,24310,44,1,1,1,1,1,1,

%U 362880,1,92378,127,5,1,1,1,1,1,1,3628800,1,352716,325,27,1,1,1,1,1,1,1

%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, northeast or northwest 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.......1........1

%C ......1.3.10.35.126.462.1716.6435.24310.92378.352716.1352078.5200300.20058300

%C ......2.2..2..2...2...5...14...44...127...325....779....1794....3988.....8830

%C ......6.1..1..1...1...1....1....5....27...147....716....3088...11526....39526

%C .....24.1..1..1...1...1....1....1.....1.....9.....65.....624....5309....38578

%C ....120.1..1..1...1...1....1....1.....1.....1......1......15.....192.....3064

%C ....720.1..1..1...1...1....1....1.....1.....1......1.......1.......1.......34

%C ...5040.1..1..1...1...1....1....1.....1.....1......1.......1.......1........1

%C ..40320.1..1..1...1...1....1....1.....1.....1......1.......1.......1

%C .362880.1..1..1...1...1....1....1.....1.....1......1.......1

%H R. H. Hardin, <a href="/A267425/b267425.txt">Table of n, a(n) for n = 1..230</a>

%e Some solutions for n=4 k=9

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

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

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

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

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

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

%Y Row 3 is A266995.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 14 2016