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

1,1

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

Links

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

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.

Example

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

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.

Sequence in context: A194420 A367952 A277823 * A118519 A282762 A089757

Adjacent sequences: A233152 A233153 A233154 * A233156 A233157 A233158

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 05 2013

Status

approved