A230533 T(n,k)=Number of nXk 0..6 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 7, and upper left element zero

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 272, 52, 0, 0, 0, 2, 1738, 35170, 35170, 1738, 2, 0, 0, 8, 18106, 1003084, 3535192, 1003084, 18106, 8, 0, 0, 32, 197916, 29871142, 286234664, 286234664, 29871142, 197916, 32, 0, 0, 120, 2076832

Offset

1,24

Comments

Table starts

.0.0......0........0.........0.........0...........0.........0.......0...0.0

.0.0......0........0.........0.........0...........2.........8......32.120

.0.0......0........0........52......1738.......18106....197916.2076832

.0.0......0......272.....35170...1003084....29871142.868791100

.0.0.....52....35170...3535192.286234664.22890686508

.0.0...1738..1003084.286234664

.0.2..18106.29871142

.0.8.197916

Links

R. H. Hardin, Table of n, a(n) for n = 1..60

Formula

Empirical for column k:

k=2: a(n) = 4*a(n-1) -4*a(n-3) -8*a(n-4) -12*a(n-5) -17*a(n-6) -10*a(n-7)

k=3: [order 64]

Example

Some solutions for n=4 k=4
..0..6..3..2....0..1..2..3....0..1..2..3....0..1..2..3....0..1..0..6
..1..5..4..1....6..3..5..4....6..5..4..4....6..5..1..4....6..2..4..5
..2..3..6..0....5..4..6..0....1..2..3..5....3..4..0..5....4..3..3..2
..3..4..5..4....2..3..2..1....0..1..0..6....2..1..0..6....5..6..0..1

Crossrefs

Sequence in context: A236517 A320556 A252335 * A235654 A118328 A079414

Adjacent sequences: A230530 A230531 A230532 * A230534 A230535 A230536

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 22 2013

Status

approved