A232948 T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically or antidiagonally, and top left element zero.

1, 3, 3, 9, 17, 9, 27, 99, 99, 27, 81, 577, 1163, 577, 81, 243, 3363, 13707, 13707, 3363, 243, 729, 19601, 161621, 328989, 161621, 19601, 729, 2187, 114243, 1905737, 7915555, 7915555, 1905737, 114243, 2187, 6561, 665857, 22471303, 190528543

Offset

1,2

Comments

Table starts

.....1........3...........9.............27.................81

.....3.......17..........99............577...............3363

.....9.......99........1163..........13707.............161621

....27......577.......13707.........328989............7915555

....81.....3363......161621........7915555..........389997789

...243....19601.....1905737......190528543........19245039957

...729...114243....22471303.....4586348177.......950054488141

..2187...665857...264968059...110402289283.....46905123394619

..6561..3880899..3124343613..2657600587981...2315805078150557

.19683.22619537.36840376337.63973693477099.114336803085406731

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1)

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

k=3: a(n) = 13*a(n-1) -15*a(n-2) +9*a(n-3) -2*a(n-4) for n>5, A232943.

k=4: [order 10] for n>11, A232944.

k=5: [order 21] for n>23, A232945.

k=6: [order 57] for n>59

Example

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

Crossrefs

Column 1 is A000244(n-1)

Column 2 is A001541

Sequence in context: A100744 A331519 A285883 * A241357 A217450 A089892

Adjacent sequences: A232945 A232946 A232947 * A232949 A232950 A232951

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 02 2013

Status

approved