A232376 T(n,k)=Number of nXk 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal

1, 2, 1, 4, 14, 1, 8, 74, 58, 1, 14, 296, 586, 230, 1, 26, 1130, 4404, 4550, 934, 1, 48, 4682, 32722, 63744, 36574, 3794, 1, 88, 19448, 259458, 927706, 957232, 292122, 15354, 1, 162, 79592, 2046700, 14326374, 27133338, 14297980, 2324142, 62266, 1, 298, 326810

Offset

1,2

Comments

Table starts

.1.......2..........4............8..............14.................26

.1......14.........74..........296............1130...............4682

.1......58........586.........4404...........32722.............259458

.1.....230.......4550........63744..........927706...........14326374

.1.....934......36574.......957232........27133338..........825606450

.1....3794.....292122.....14297980.......789866870........47301712998

.1...15354....2324142....213082596.....22946925502......2706080691402

.1...62266...18574882...3180405572....667514680522....154987416800398

.1..252346..148225606..47457708756..19413840326186...8875595994390694

.1.1022806.1182879814.708101568772.564595278464614.508249649361525870

Links

R. H. Hardin, Table of n, a(n) for n = 1..160

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +7*a(n-2) +6*a(n-3) -2*a(n-4) -3*a(n-5) +2*a(n-6) +a(n-7)

k=3: [order 15]

k=4: [order 22]

k=5: [order 64]

Empirical for row n:

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

n=2: [order 8] for n>9

n=3: [order 13] for n>14

n=4: [order 60] for n>61

Example

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

Crossrefs

Row 1 is A135491(n-1)

Sequence in context: A066409 A006173 A102055 * A350739 A263575 A162977

Adjacent sequences: A232373 A232374 A232375 * A232377 A232378 A232379

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 23 2013

Status

approved