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A232955
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, and top left element zero
13
1, 3, 4, 9, 21, 16, 27, 129, 147, 64, 81, 771, 1881, 1029, 256, 243, 4629, 22971, 27441, 7203, 1024, 729, 27771, 283131, 685251, 400329, 50421, 4096, 2187, 166629, 3484893, 17429409, 20442651, 5840289, 352947, 16384, 6561, 999771, 42904365, 442227825
OFFSET
1,2
COMMENTS
Table starts
......1.........3............9..............27.................81
......4........21..........129.............771...............4629
.....16.......147.........1881...........22971.............283131
.....64......1029........27441..........685251...........17429409
....256......7203.......400329........20442651.........1074244299
...1024.....50421......5840289.......609853251........66226131273
...4096....352947.....85202361.....18193384251......4082986991091
..16384...2470629...1242993681....542752261251....251727862281441
..65536..17294403..18133691049..16191600916251..15519780149309307
.262144.121060821.264547403649.483034266181251.956841601733733945
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 4*a(n-1)
k=2: a(n) = 7*a(n-1)
k=3: a(n) = 15*a(n-1) -6*a(n-2)
k=4: a(n) = 31*a(n-1) -35*a(n-2) +5*a(n-3)
k=5: [order 10]
k=6: [order 21]
Empirical for row n:
n=1: a(n) = 3*a(n-1)
n=2: a(n) = 5*a(n-1) +6*a(n-2)
n=3: a(n) = 12*a(n-1) +7*a(n-2) -40*a(n-3) +12*a(n-4)
n=4: [order 10]
n=5: [order 26] for n>27
n=6: [order 86] for n>87
EXAMPLE
Some solutions for n=3 k=4
..0..2..3..2....0..1..3..3....0..1..0..2....0..1..0..0....0..2..0..2
..2..2..3..3....0..1..1..1....3..2..0..1....0..2..0..0....2..0..2..2
..0..2..3..3....0..1..0..0....2..2..3..2....0..2..0..2....1..0..2..0
CROSSREFS
Column 1 is A000302(n-1)
Column 2 is A169634(n-1)
Row 1 is A000244(n-1)
Sequence in context: A049978 A324764 A092763 * A116868 A049976 A032789
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 02 2013
STATUS
approved