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A265928
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T(n,k)=Number of nXk 0..4 arrays with the absolute differences of each element with its with horizontal and antidiagonal neighbors unique.
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15
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5, 25, 25, 92, 340, 125, 340, 1740, 4616, 625, 1252, 9016, 17936, 62696, 3125, 4616, 44916, 72772, 174000, 851496, 15625, 17012, 223788, 273616, 542940, 1671744, 11564952, 78125, 62696, 1119424, 1042020, 1546496, 4044156, 15962560, 157071768
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OFFSET
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1,1
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COMMENTS
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Table starts
.......5...........25...........92.........340........1252........4616
......25..........340.........1740........9016.......44916......223788
.....125.........4616........17936.......72772......273616.....1042020
.....625........62696.......174000......542940.....1546496.....4697060
....3125.......851496......1671744.....4044156.....8821464....22093736
...15625.....11564952.....15962560....30029860....51986544...112139348
...78125....157071768....152267520...225444912...309447168...579039920
..390625...2133318088...1451371264..1691502456..1904101280..3147755448
.1953125..28974227016..13834836992.12779302796.11662822720.16695518060
.9765625.393521606584.131883277312.96726712256.73936333840.93517706688
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 5*a(n-1)
k=2: [order 8]
k=3: [order 10] for n>13
k=4: [order 28] for n>32
k=5: [order 31] for n>39
k=6: [order 42] for n>50
k=7: [order 48] for n>55
Empirical for row n:
n=1: [linear recurrence of order 8] for n>9
n=2: [order 55] for n>59
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EXAMPLE
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Some solutions for n=3 k=4
..2..0..0..1....1..1..3..0....1..0..3..2....0..1..1..4....3..4..1..0
..4..4..1..0....2..4..4..1....4..3..0..1....3..0..0..2....0..1..3..3
..3..3..0..1....0..3..1..0....1..0..3..4....4..1..1..4....4..4..1..0
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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