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A275565
T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,0) (-1,2) or (0,-2) and new values introduced in order 0..2.
12
1, 2, 2, 3, 14, 3, 6, 36, 54, 6, 12, 96, 126, 216, 12, 24, 288, 294, 504, 864, 24, 48, 864, 672, 1176, 1872, 3456, 48, 96, 2592, 1536, 3192, 4056, 7200, 13824, 96, 192, 7776, 3552, 8664, 13104, 15000, 27360, 55296, 192, 384, 23328, 8214, 23712, 42336, 57600
OFFSET
1,2
COMMENTS
Table starts
...1......2.......3.......6.......12........24.........48..........96
...2.....14......36......96......288.......864.......2592........7776
...3.....54.....126.....294......672......1536.......3552........8214
...6....216.....504....1176.....3192......8664......23712.......64896
..12....864....1872....4056....13104.....42336.....138600......453750
..24...3456....7200...15000....57600....221184.....867456.....3402054
..48..13824...27360...54150...248520...1140576....5360184....25190406
..96..55296..104256..196566..1075140...5880600...33275880...188294424
.192.221184..397440..714150..4663710..30456054..206892990..1405458150
.384.884736.1513728.2589894.20186982.157347846.1286374716.10516571736
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) for n>3
k=2: a(n) = 4*a(n-1) for n>3
k=3: a(n) = 2*a(n-1) +8*a(n-2) -16*a(n-4) for n>5
k=4: [order 10] for n>11
k=5: [order 32] for n>34
k=6: [order 35] for n>37
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>4
n=3: a(n) = 3*a(n-1) -5*a(n-3) +a(n-4) +7*a(n-5) -5*a(n-6) +2*a(n-8) -a(n-9) for n>10
n=4: [order 25] for n>28
n=5: [order 63] for n>66
EXAMPLE
Some solutions for n=4 k=4
..0..1..2..2. .0..1..1..2. .0..1..2..2. .0..1..2..0. .0..1..2..0
..1..0..0..1. .0..1..2..0. .1..0..0..2. .0..1..1..2. .1..1..2..2
..2..2..1..1. .1..2..2..1. .1..0..0..1. .2..0..1..1. .1..0..0..2
..2..2..1..0. .1..0..0..1. .2..2..1..1. .2..2..0..1. .2..0..0..1
CROSSREFS
Column 1 is A003945(n-2).
Column 2 is A208428.
Row 1 is A003945(n-2).
Sequence in context: A073828 A338523 A189312 * A275090 A373310 A274983
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Aug 01 2016
STATUS
approved