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A274803
T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) (0,-1) or (-1,0) and new values introduced in order 0..2.
7
1, 1, 1, 2, 3, 2, 4, 8, 8, 4, 8, 22, 30, 22, 8, 16, 60, 112, 112, 60, 16, 32, 164, 420, 596, 420, 164, 32, 64, 448, 1572, 3104, 3104, 1572, 448, 64, 128, 1224, 5888, 16328, 22988, 16328, 5888, 1224, 128, 256, 3344, 22048, 85504, 169328, 169328, 85504, 22048, 3344
OFFSET
1,4
COMMENTS
Table starts
...1....1......2........4.........8..........16...........32.............64
...1....3......8.......22........60.........164..........448...........1224
...2....8.....30......112.......420........1572.........5888..........22048
...4...22....112......596......3104.......16328........85504.........448656
...8...60....420.....3104.....22988......169328......1252608........9243332
..16..164...1572....16328....169328.....1774372.....18476064......193292660
..32..448...5888....85504...1252608....18476064....273764292.....4044928780
..64.1224..22048...448656...9243332...193292660...4044928780....85071335388
.128.3344..82568..2352080..68301192..2016460140..59936952948..1784175028356
.256.9136.309200.12335680.504334580.21072173792.886462457880.37524080122192
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) for n>2
k=2: a(n) = 2*a(n-1) +2*a(n-2)
k=3: a(n) = 2*a(n-1) +6*a(n-2) +2*a(n-3)
k=4: a(n) = 2*a(n-1) +15*a(n-2) +11*a(n-3) -2*a(n-4) -2*a(n-5)
k=5: a(n) = 2*a(n-1) +35*a(n-2) +42*a(n-3) -41*a(n-4) -60*a(n-5) -23*a(n-6) -2*a(n-7)
k=6: [order 14] for n>15
k=7: [order 25] for n>26
EXAMPLE
Some solutions for n=4 k=4
..0..1..0..2. .0..1..2..0. .0..1..2..1. .0..1..2..1. .0..1..0..1
..1..2..1..0. .1..0..1..2. .1..2..1..2. .1..0..1..0. .1..0..1..2
..0..1..0..1. .0..1..2..1. .2..1..0..1. .2..1..2..1. .0..1..2..1
..2..0..1..2. .1..0..1..0. .1..2..1..0. .0..2..1..0. .1..2..1..2
CROSSREFS
Column 1 is A000079(n-2).
Column 2 is A028859(n-1).
Sequence in context: A105070 A154578 A059576 * A274749 A247936 A231150
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 07 2016
STATUS
approved