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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 7
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 02 2013
STATUS
approved

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Last modified February 25 19:44 EST 2024. Contains 370332 sequences. (Running on oeis4.)