A233155 T(n,k) = Number of n X k 0..2 arrays with no element x(i,j) adjacent to value 2-x(i,j) horizontally or antidiagonally.

3, 6, 9, 12, 24, 27, 24, 72, 96, 81, 48, 216, 432, 384, 243, 96, 648, 1944, 2592, 1536, 729, 192, 1944, 8856, 17496, 15552, 6144, 2187, 384, 5832, 40392, 121176, 157464, 93312, 24576, 6561, 768, 17496, 184248, 842616, 1658232, 1417176, 559872, 98304, 19683

Offset: 1

Author

R. H. Hardin, Dec 05 2013

Keywords

• nonn
• tabl

Comments

Table starts

.....3.......6........12.........24...........48.............96

.....9......24........72........216..........648...........1944

....27......96.......432.......1944.........8856..........40392

....81.....384......2592......17496.......121176.........842616

...243....1536.....15552.....157464......1658232.......17587584

...729....6144.....93312....1417176.....22692312......367125912

..2187...24576....559872...12754584....310536504.....7663517136

..6561...98304...3359232..114791256...4249585944...159971190624

.19683..393216..20155392.1033121304..58154132088..3339300422232

.59049.1572864.120932352.9298091736.795819434328.69705848287656

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..390

Crossrefs

Column 1 is A000244.

Column 2 is A002023(n-1).

Column 3 is 2*A000400.

Column 4 is 3*A055275.

Row 1 is A003945.

Row 2 is A005051(n-1) for n>1.

Formula

Empirical for column k:

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

k=2: a(n) = 4*a(n-1).

k=3: a(n) = 6*a(n-1).

k=4: a(n) = 9*a(n-1).

k=5: a(n) = 15*a(n-1) -18*a(n-2).

k=6: a(n) = 25*a(n-1) -90*a(n-2) +81*a(n-3).

k=7: a(n) = 42*a(n-1) -351*a(n-2) +972*a(n-3) -810*a(n-4).

Empirical for row n:

n=1: a(n) = 2*a(n-1).

n=2: a(n) = 3*a(n-1) for n>2.

n=3: a(n) = 5*a(n-1) -2*a(n-2) for n>4.

n=4: a(n) = 9*a(n-1) -15*a(n-2) +6*a(n-3) for n>7.

n=5: [order 7] for n>11.

n=6: [order 9] for n>15.

n=7: [order 27] for n>33.