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

1,2

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

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

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

Adjacent sequences: A232952 A232953 A232954 * A232956 A232957 A232958

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 02 2013

Status

approved