A267655 - OEIS

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

%S 1,1,1,1,3,1,1,10,4,1,1,35,17,3,1,1,126,66,23,3,1,1,462,324,123,21,3,

%T 1,1,1716,1565,657,221,17,3,1,1,6435,7908,4765,1811,268,17,3,1,1,

%U 24310,41440,36055,13359,4585,203,17,3,1,1,92378,219394,256836,129319,55105,7672,167

%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 north 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

%C .1.3.10..35..126....462......1716.......6435.......24310.......92378

%C .1.4.17..66..324...1565......7908......41440......219394.....1181538

%C .1.3.23.123..657...4765.....36055.....256836.....1888443....14723754

%C .1.3.21.221.1811..13359....129319....1586523....18730678...199349073

%C .1.3.17.268.4585..55105....569689....7128794...126811891..2572337388

%C .1.3.17.203.7672.201362...3562990...52241496...855234512.19809675462

%C .1.3.17.167.7145.467919..18784855..491779927.10416831490

%C .1.3.17.167.5356.608250..61856471.3779928997

%C .1.3.17.167.4640.513398.115115782

%C Empirical: column k descends to a constant at n=2k, the final constant for k=1..7 being 1 3 17 167 4640 348814 77196948

%H R. H. Hardin, <a href="/A267655/b267655.txt">Table of n, a(n) for n = 1..142</a>

%e Some solutions for n=6 k=4

%e ..0..0..2..3....0..1..2..3....0..1..2..4....0..2..3..5....0..2..2..4

%e ..0..1..2..4....1..1..2..4....0..1..3..5....1..2..4..5....1..2..3..5

%e ..0..1..3..5....1..2..3..5....1..2..4..5....2..3..4..0....1..3..4..5

%e ..1..2..4..5....2..3..4..0....2..3..4..5....2..3..5..0....2..3..5..0

%e ..1..3..4..5....3..4..5..0....2..3..5..0....3..4..0..1....3..4..0..1

%e ..2..3..4..5....4..5..5..0....3..4..0..1....4..5..1..1....4..5..0..1

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

%Y Row 3 is A266862.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 19 2016