A233098 T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order

1, 2, 3, 5, 11, 10, 14, 65, 74, 36, 41, 386, 941, 515, 136, 122, 2315, 11486, 13721, 3602, 528, 365, 13886, 141566, 342626, 200165, 25211, 2080, 1094, 83315, 1742447, 8714705, 10221326, 2920145, 176474, 8256, 3281, 499886, 21452183, 221113913

Offset

1,2

Comments

Table starts

......1........2............5..............14.................41

......3.......11...........65.............386...............2315

.....10.......74..........941...........11486.............141566

.....36......515........13721..........342626............8714705

....136.....3602.......200165........10221326..........537122150

....528....25211......2920145.......304926626........33113065637

...2080...176474.....42601181......9096692126......2041493495546

...8256..1235315....621496841....271376130626....125863931140721

..32896..8647202...9066845525...8095800458126...7759890074654654

.131328.60530411.132273701825.241517133090626.478420800866866973

Links

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

Formula

Empirical for column k:

k=1: a(n) = 6*a(n-1) -8*a(n-2)

k=2: a(n) = 8*a(n-1) -7*a(n-2)

k=3: a(n) = 16*a(n-1) -21*a(n-2) +6*a(n-3)

k=4: a(n) = 31*a(n-1) -35*a(n-2) +5*a(n-3)

k=5: [order 11]

k=6: [order 22]

Empirical for row n:

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

n=2: a(n) = 6*a(n-1) +a(n-2) -6*a(n-3) for n>4

n=3: a(n) = 13*a(n-1) -5*a(n-2) -47*a(n-3) +52*a(n-4) -12*a(n-5) for n>6

n=4: [order 11] for n>12

n=5: [order 27] for n>28

n=6: [order 87] for n>88

Example

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

Crossrefs

Column 1 is A007582(n-1)

Column 2 is A199417(n-1)

Row 1 is A007051(n-1)

Sequence in context: A112037 A087583 A372284 * A258975 A111214 A272197

Adjacent sequences: A233095 A233096 A233097 * A233099 A233100 A233101

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 04 2013

Status

approved