A230513 T(n,k)=Number of nXk 0..7 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 8, and upper left element zero

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 16, 2, 0, 0, 8, 170, 170, 8, 0, 0, 32, 1716, 4648, 1716, 32, 0, 0, 118, 18588, 129874, 129874, 18588, 118, 0, 0, 440, 215314, 4038314, 10308020, 4038314, 215314, 440, 0, 0, 1664, 2510424, 129829460, 918775180, 918775180

Offset

1,12

Comments

Table starts

.0...0.......0.........0.........0.........0...........0..........0........0

.0...0.......0.........2.........8........32.........118........440.....1664

.0...0......16.......170......1716.....18588......215314....2510424.29109876

.0...2.....170......4648....129874...4038314...129829460.4177480490

.0...8....1716....129874..10308020.918775180.84808478358

.0..32...18588...4038314.918775180

.0.118..215314.129829460

.0.440.2510424

Links

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

Formula

Empirical for column k:

k=2: a(n) = 5*a(n-1) -4*a(n-2) -5*a(n-3) +9*a(n-4) +12*a(n-5)

k=3: [order 32]

Example

Some solutions for n=3 k=4
..0..7..6..5....0..7..0..1....0..7..6..5....0..1..2..1....0..1..0..1
..1..4..5..4....1..6..5..2....1..2..3..4....7..6..3..2....7..2..3..2
..2..3..2..1....2..3..4..3....0..7..2..1....4..5..4..1....6..5..4..1

Crossrefs

Sequence in context: A031361 A155955 A221076 * A300138 A362884 A217028

Adjacent sequences: A230510 A230511 A230512 * A230514 A230515 A230516

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 21 2013

Status

approved