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.

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

Author

R. H. Hardin, Dec 02 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000302(n-1)

Column 2 is A169634(n-1)

Row 1 is A000244(n-1)

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