A232161 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, vertically or antidiagonally, and no adjacent values equal

1, 2, 2, 4, 18, 4, 8, 62, 62, 8, 14, 218, 290, 218, 14, 26, 746, 1284, 1284, 746, 26, 48, 2600, 5902, 7770, 5902, 2600, 48, 88, 9004, 27086, 46702, 46702, 27086, 9004, 88, 162, 31262, 124436, 286770, 382996, 286770, 124436, 31262, 162, 298, 108492, 572080

Offset

1,2

Comments

Table starts

...1......2........4.........8..........14...........26.............48

...2.....18.......62.......218.........746.........2600...........9004

...4.....62......290......1284........5902........27086.........124436

...8....218.....1284......7770.......46702.......286770........1767266

..14....746.....5902.....46702......382996......3183932.......26694774

..26...2600....27086....286770.....3183932.....36275078......415332300

..48...9004...124436...1767266....26694774....415332300.....6564512068

..88..31262...572080..10830650...223026806...4764939084...103384156384

.162.108492..2629946..66701686..1869037596..54785401618..1636124088162

.298.376566.12090710.410364610.15673051556.629979277720.25973583237174

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

k=2: [order 10] for n>11

k=3: [order 30] for n>33

k=4: [order 94] for n>97

Example

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

Crossrefs

Column 1 is A135491(n-1)

Sequence in context: A051285 A079556 A367681 * A335684 A052628 A006853

Adjacent sequences: A232158 A232159 A232160 * A232162 A232163 A232164

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 19 2013

Status

approved