A267222 - OEIS

%I #6 Aug 12 2016 06:55:34

%S 1,1,1,1,0,2,1,0,3,6,1,0,8,35,24,1,0,17,458,889,120,1,0,34,7137,63600,

%T 52759,720,1,0,68,127262,6574092,46185656,4249084,5040,1,0,164,

%U 2409733,807737754,57528166669,53918229032,454920734,40320,1,0,385,47615756

%N T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with no element 1 greater than its west, northeast or southeast neighbor modulo n and the upper left element equal to 0.

%C Table starts

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

%C .....1.........0...........0...........0.........0............0........0...0.0

%C .....2.........3...........8..........17........34...........68......164.385

%C .....6........35.........458........7137....127262......2409733.47615756

%C ....24.......889.......63600.....6574092.807737754.109215090103

%C ...120.....52759....46185656.57528166669

%C ...720...4249084.53918229032

%C ..5040.454920734

%C .40320

%H R. H. Hardin, <a href="/A267222/b267222.txt">Table of n, a(n) for n = 1..50</a>

%e Some solutions for n=4 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,6

%A _R. H. Hardin_, Jan 12 2016