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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. 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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 05 2013
STATUS
approved

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Last modified June 25 15:24 EDT 2024. Contains 373705 sequences. (Running on oeis4.)