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A233155 T(n,k)=Number of nXk 0..2 arrays with no element x(i,j) adjacent to value 2-x(i,j) horizontally or antidiagonally 10
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 (list; table; graph; refs; listen; history; text; internal format)
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: A143829 A194420 A277823 * A118519 A282762 A089757

Adjacent sequences:  A233152 A233153 A233154 * A233156 A233157 A233158

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 05 2013

STATUS

approved

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Last modified September 24 17:33 EDT 2021. Contains 347651 sequences. (Running on oeis4.)