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A233217
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T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order
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14
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1, 2, 3, 6, 23, 11, 23, 376, 452, 48, 99, 7222, 35446, 10313, 236, 452, 147019, 3054973, 3638416, 249062, 1248, 2136, 3054973, 268289572, 1340889772, 380283286, 6147803, 6896, 10313, 63927526, 23644611625, 496475792293, 591021089923, 39892988056
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OFFSET
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1,2
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COMMENTS
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Table starts
....1.........2.............6.................23.....................99
....3........23...........376...............7222.................147019
...11.......452.........35446............3054973..............268289572
...48.....10313.......3638416.........1340889772...........496475792293
..236....249062.....380283286.......591021089923........919538740854193
.1248...6147803...39892988056....260625046992322....1703198747507336644
.6896.152986472.4187991850726.114934898294104873.3154729081272072714436
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..161
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FORMULA
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Empirical for column k:
k=1: a(n) = 12*a(n-1) -44*a(n-2) +48*a(n-3)
k=2: a(n) = 35*a(n-1) -259*a(n-2) +225*a(n-3)
k=3: a(n) = 127*a(n-1) -2331*a(n-2) +2205*a(n-3)
k=4: a(n) = 491*a(n-1) -22099*a(n-2) +21609*a(n-3)
k=5: a(n) = 1975*a(n-1) -228357*a(n-2) +1804281*a(n-3) -4170978*a(n-4) +2593080*a(n-5)
k=6: [order 7]
k=7: [order 11]
Empirical for row n:
n=1: a(n) = 9*a(n-1) -23*a(n-2) +15*a(n-3)
n=2: a(n) = 29*a(n-1) -175*a(n-2) +147*a(n-3) for n>4
n=3: a(n) = 111*a(n-1) -2128*a(n-2) +10532*a(n-3) -17559*a(n-4) +9045*a(n-5) for n>7
n=4: [order 9] for n>12
n=5: [order 19] for n>23
n=6: [order 42] for n>47
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EXAMPLE
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Some solutions for n=3 k=4
..0..0..0..1....0..0..0..1....0..0..0..1....0..0..0..1....0..0..0..1
..2..1..2..1....0..1..5..1....0..2..2..1....2..0..0..0....0..2..1..3
..2..0..2..2....1..5..1..0....4..0..1..0....0..1..3..5....2..0..0..2
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CROSSREFS
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Column 1 is A233162(n+1)
Row 1 is A233106
Sequence in context: A303584 A261014 A000616 * A261963 A183179 A018300
Adjacent sequences: A233214 A233215 A233216 * A233218 A233219 A233220
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Dec 06 2013
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STATUS
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approved
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