login
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 southwest neighbors modulo n and the upper left element equal to 0.
10

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

%S 1,1,1,1,3,2,1,10,2,6,1,35,6,2,24,1,126,31,3,2,120,1,462,141,15,3,2,

%T 720,1,1716,550,170,3,3,2,5040,1,6435,2046,1614,55,3,3,2,40320,1,

%U 24310,8149,11048,1326,8,3,3,2,362880,1,92378,34902,60954,27712,279,8,3,3,2,3628800

%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 southwest 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

%C ......1.3.10.35.126..462..1716...6435....24310......92378.......352716

%C ......2.2..6.31.141..550..2046...8149....34902.....152001.......652150

%C ......6.2..3.15.170.1614.11048..60954...299110....1494098......8772195

%C .....24.2..3..3..55.1326.27712.392186..4032703...32764364....226023332

%C ....120.2..3..3...8..279.15686.711359.21893719..463755018...7207021169

%C ....720.2..3..3...8...17..2033.279070.27767384.1883165721..86034010064

%C ...5040.2..3..3...8...17....76..21772..7353006.1673476119.250936616799

%C ..40320.2..3..3...8...17....76....424...345843

%C .362880.2..3..3...8...17....76....424

%H R. H. Hardin, <a href="/A267562/b267562.txt">Table of n, a(n) for n = 1..161</a>

%e Some solutions for n=4 k=4

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

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

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

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

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

%Y Diagonal is A267552.

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

%Y Row 3 is A267073.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 17 2016