A231108 T(n,k)=Number of nXk 0..3 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.

0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 6, 8, 0, 0, 0, 20, 48, 42, 0, 0, 0, 68, 286, 438, 208, 0, 0, 0, 230, 1748, 4674, 3936, 1042, 0, 0, 0, 778, 10734, 53530, 75346, 35430, 5208, 0, 0, 0, 2632, 65934, 616562, 1608428, 1217338, 318864, 26042, 0, 0, 0, 8904, 404984, 7084870

Offset

1,8

Comments

Table starts

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

.0.0.....2.......6........20..........68...........230.............778

.0.0.....8......48.......286........1748.........10734...........65934

.0.0....42.....438......4674.......53530........616562.........7084870

.0.0...208....3936.....75346.....1608428......34716434.......745738376

.0.0..1042...35430...1217338....48463174....1961000570.....78805506362

.0.0..5208..318864..19662930..1459796386..110728004898...8325135556908

.0.0.26042.2869782.317613674.43973372728.6252665856636.879549454424322

Links

R. H. Hardin, Table of n, a(n) for n = 1..179

Formula

Empirical for column k:

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

k=4: a(n) = 8*a(n-1) +9*a(n-2)

k=5: a(n) = 14*a(n-1) +35*a(n-2) -4*a(n-3) +4*a(n-4) +32*a(n-5) -32*a(n-6)

k=6: [order 17] for n>18

k=7: [order 32] for n>34

Empirical for row n:

n=2: a(n) = 3*a(n-1) +a(n-2) +a(n-3)

n=3: [order 12] for n>16

n=4: [order 51] for n>56

Example

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

Crossrefs

Row 2 is A231057(n-1)

Sequence in context: A066503 A389162 A057385 * A231285 A268729 A182317

Adjacent sequences: A231105 A231106 A231107 * A231109 A231110 A231111

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 03 2013

Status

approved