A230730 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

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, 2790, 9760, 6212, 0, 0, 0, 0, 506, 32094, 287616, 389148, 95412, 0, 0, 0, 0, 2144, 376934, 9059304, 31533840, 15237056, 1459082, 0, 0, 0, 0, 9030, 4362078, 292876646

Offset

1,12

Comments

Table starts

.0.0.0........0...........0..............0.................0

.0.0.0........2...........8.............30...............120

.0.0.0.......30.........260...........2790.............32094

.0.0.0......396........9760.........287616...........9059304

.0.0.0.....6212......389148.......31533840........2754151172

.0.0.0....95412....15237056.....3392436180......819577760474

.0.0.0..1459082...597115044...364767453384...243012308326942

.0.0.0.22379112.23414415888.39242855355538.72110003488927180

Links

R. H. Hardin, Table of n, a(n) for n = 1..125

Formula

Empirical for column k:

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)

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

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

Empirical for row n:

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

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

Example

Some solutions for n=4 k=4
..0..1..0..3....0..1..2..3....0..1..4..5....0..1..0..3....0..1..2..3
..2..3..4..5....0..5..4..3....2..3..0..5....2..3..4..3....0..5..4..3
..0..1..0..5....0..1..2..3....2..1..0..5....2..5..2..5....4..3..0..5
..2..3..4..3....0..5..4..3....0..3..4..3....0..1..0..5....2..1..0..5

Crossrefs

Row 2 is A230588(n-1)

Sequence in context: A364055 A184366 A230614 * A299905 A225783 A135468

Adjacent sequences: A230727 A230728 A230729 * A230731 A230732 A230733

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 28 2013

Status

approved