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A274749
T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.
11
1, 1, 1, 2, 3, 2, 4, 8, 9, 4, 8, 22, 34, 27, 8, 16, 60, 133, 144, 81, 16, 32, 164, 518, 813, 610, 243, 32, 64, 448, 2017, 4554, 4967, 2584, 729, 64, 128, 1224, 7858, 25585, 40242, 30349, 10946, 2187, 128, 256, 3344, 30605, 143634, 327123, 355504, 185435, 46368
OFFSET
1,4
COMMENTS
Table starts
...1.....1......2........4..........8...........16............32
...1.....3......8.......22.........60..........164...........448
...2.....9.....34......133........518.........2017..........7858
...4....27....144......813.......4554........25585........143634
...8....81....610.....4967......40242.......327123.......2661918
..16...243...2584....30349.....355504......4190533......49475642
..32...729..10946...185435....3140840.....53680592.....920432562
..64..2187..46368..1133025...27748676....687685512...17123659885
.128..6561.196418..6922887..245154340...8809672678..318581114142
.256.19683.832040.42299477.2165891856.112857546696.5927090659144
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) for n>2
k=2: a(n) = 3*a(n-1)
k=3: a(n) = 4*a(n-1) +a(n-2)
k=4: a(n) = 6*a(n-1) +a(n-2) -2*a(n-3) for n>4
k=5: a(n) = 9*a(n-1) -14*a(n-3) +10*a(n-4) -2*a(n-5) for n>6
k=6: [order 9] for n>11
k=7: [order 13] for n>15
Empirical for row n:
n=1: a(n) = 2*a(n-1) for n>2
n=2: a(n) = 2*a(n-1) +2*a(n-2)
n=3: a(n) = 2*a(n-1) +7*a(n-2) +2*a(n-3) -2*a(n-4)
n=4: [order 8]
n=5: [order 16] for n>17
n=6: [order 36] for n>38
n=7: [order 80] for n>83
EXAMPLE
Some solutions for n=4 k=4
..0..1..0..1. .0..1..0..2. .0..1..2..0. .0..1..0..2. .0..1..0..2
..1..0..1..2. .1..0..2..0. .1..2..1..2. .1..2..1..0. .1..0..1..0
..0..1..2..1. .0..1..0..2. .2..1..0..1. .2..1..0..1. .0..2..0..1
..2..0..1..2. .2..0..2..0. .0..2..1..2. .1..0..1..0. .2..0..2..0
CROSSREFS
Column 1 is A000079(n-2).
Column 2 is A000244(n-1).
Column 3 is A014445.
Row 1 is A000079(n-2).
Row 2 is A028859(n-1).
Sequence in context: A154578 A059576 A274803 * A247936 A231150 A274858
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 04 2016
STATUS
approved