A230469 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero

0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 36, 114, 8, 0, 0, 216, 2398, 1384, 30, 0, 0, 1260, 35052, 76518, 16926, 108, 0, 0, 6912, 552720, 3062214, 2593962, 212124, 386, 0, 0, 38340, 8724560, 131421154, 281740616, 89087722, 2647098, 1376, 0, 0, 213192, 138661614

Offset

1,9

Comments

Table starts

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

.0....0........0...........36.............216...............1260

.0....2......114.........2398...........35052.............552720

.0....8.....1384........76518.........3062214..........131421154

.0...30....16926......2593962.......281740616........33169633760

.0..108...212124.....89087722.....26096227960......8449174734112

.0..386..2647098...3045192312...2412390974650...2147475302085202

.0.1376.33046400.104165339046.223089594072370.545932535826768684

Links

R. H. Hardin, Table of n, a(n) for n = 1..126

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

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

k=3: [order 7]

k=4: [order 21]

k=5: [order 68]

Empirical for row n:

n=1: a(n) = a(n-1)

n=2: a(n) = 6*a(n-1) -a(n-2) -12*a(n-3) +20*a(n-4) +24*a(n-5)

n=3: [order 16] for n>17

n=4: [order 57] for n>58

Example

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

Crossrefs

Column 2 is A230269

Sequence in context: A179072 A073111 A229685 * A004076 A365974 A013369

Adjacent sequences: A230466 A230467 A230468 * A230470 A230471 A230472

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 20 2013

Status

approved