login
T(n,k)=Number of nXk 0..5 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 6, and upper left element zero
9

%I #4 Oct 28 2013 19:59:51

%S 0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,8,30,0,0,0,0,30,260,396,0,0,0,0,120,

%T 2790,9760,6212,0,0,0,0,506,32094,287616,389148,95412,0,0,0,0,2144,

%U 376934,9059304,31533840,15237056,1459082,0,0,0,0,9030,4362078,292876646

%N T(n,k)=Number of nXk 0..5 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 6, and upper left element zero

%C Table starts

%C .0.0.0........0...........0..............0.................0

%C .0.0.0........2...........8.............30...............120

%C .0.0.0.......30.........260...........2790.............32094

%C .0.0.0......396........9760.........287616...........9059304

%C .0.0.0.....6212......389148.......31533840........2754151172

%C .0.0.0....95412....15237056.....3392436180......819577760474

%C .0.0.0..1459082...597115044...364767453384...243012308326942

%C .0.0.0.22379112.23414415888.39242855355538.72110003488927180

%H R. H. Hardin, <a href="/A230730/b230730.txt">Table of n, a(n) for n = 1..125</a>

%F Empirical for column k:

%F k=4: a(n) = 16*a(n-1) -12*a(n-2) +87*a(n-3) -918*a(n-4) +61*a(n-5) -a(n-6)

%F k=5: [order 7] for n>8

%F k=6: [order 50] for n>51

%F Empirical for row n:

%F n=2: a(n) = 5*a(n-1) -5*a(n-2) +5*a(n-3) +8*a(n-4) for n>5

%F n=3: [order 31] for n>34

%e Some solutions for n=4 k=4

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

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

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

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

%Y Row 2 is A230588(n-1)

%K nonn,tabl

%O 1,12

%A _R. H. Hardin_, Oct 28 2013