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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 neighbor modulo n and the upper left element equal to 0.
8

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

%S 1,1,1,1,3,2,1,10,7,6,1,35,39,27,24,1,126,265,208,138,120,1,462,1802,

%T 2386,1576,900,720,1,1716,12239,32208,29387,14830,7110,5040,1,6435,

%U 84614,445970,679735,469605,168500,66150,40320,1,24310,597601,6039160,17761798

%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 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.......7........39........265........1802.......12239.......84614

%C ......6......27.......208.......2386.......32208......445970.....6039160

%C .....24.....138......1576......29387......679735....17761798...490407156

%C ....120.....900.....14830.....469605....19027506...873319806.44064461220

%C ....720....7110....168500....8889180...651123366.54381881627

%C ...5040...66150...2247280..196362845.25708254936

%C ..40320..708120..34423760.4969038690

%C .362880.8573040.596248800

%H R. H. Hardin, <a href="/A267629/b267629.txt">Table of n, a(n) for n = 1..83</a>

%e Some solutions for n=4 k=4

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

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

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

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

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

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

%Y Row 3 is A266310.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 18 2016