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A276248
T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,1) or (0,-2) and new values introduced in order 0..2.
12
1, 2, 2, 3, 9, 5, 6, 24, 36, 14, 12, 72, 85, 144, 41, 24, 216, 279, 347, 576, 122, 48, 648, 900, 1447, 1404, 2304, 365, 96, 1944, 2837, 6372, 7316, 5671, 9216, 1094, 192, 5832, 9148, 26325, 43662, 36744, 23000, 36864, 3281, 384, 17496, 29570, 115682, 234431
OFFSET
1,2
COMMENTS
Table starts
....1......2.......3........6........12..........24...........48.............96
....2......9......24.......72.......216.........648.........1944...........5832
....5.....36......85......279.......900........2837.........9148..........29570
...14....144.....347.....1447......6372.......26325.......115682.........509750
...41....576....1404.....7316.....43662......234431......1423062........8496628
..122...2304....5671....36744....291113.....2069454.....17450554......141165944
..365...9216...23000...188696...2003694....18671229....219977330.....2410124377
.1094..36864...93204...966555..13727745...167951009...2780927371....41132001645
.3281.147456..377421..4951790..93489265..1509288801..35144231606...700435484735
.9842.589824.1529844.25428687.640009243.13609728840.446083313365.11973407175492
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 4*a(n-1) -3*a(n-2)
k=2: a(n) = 4*a(n-1) for n>2
k=3: a(n) = 5*a(n-1) -4*a(n-2) +17*a(n-3) -83*a(n-4) +54*a(n-5) +56*a(n-6) for n>9
k=4: [order 36] for n>37
k=5: [order 41] for n>45
Empirical for row n:
n=1: a(n) = 2*a(n-1) for n>3
n=2: a(n) = 3*a(n-1) for n>3
n=3: [order 14] for n>15
n=4: [order 57] for n>60
EXAMPLE
Some solutions for n=4 k=4
..0..0..1..1. .0..0..1..2. .0..0..1..1. .0..1..1..2. .0..0..1..2
..1..2..2..1. .2..0..0..1. .2..2..0..1. .2..2..0..0. .2..2..0..1
..0..1..2..2. .1..1..2..2. .0..1..2..2. .1..1..2..2. .1..1..2..2
..2..0..0..1. .0..0..1..2. .0..0..1..1. .2..0..1..1. .2..0..0..2
CROSSREFS
Column 1 is A007051(n-1).
Column 2 is A002063(n-2).
Row 1 is A003945(n-2).
Sequence in context: A274959 A143307 A278463 * A322891 A275329 A021821
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Aug 25 2016
STATUS
approved