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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
13
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 04 2013
STATUS
approved