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A265928
T(n,k)=Number of nXk 0..4 arrays with the absolute differences of each element with its with horizontal and antidiagonal neighbors unique.
15
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
OFFSET
1,1
COMMENTS
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
LINKS
FORMULA
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
EXAMPLE
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
CROSSREFS
Column 1 is A000351.
Sequence in context: A271379 A192493 A265973 * A039936 A124398 A121003
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 18 2015
STATUS
approved