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

Author

R. H. Hardin, Nov 23 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Row 1 is A135491(n-1)

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