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A240000
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T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4
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13
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2, 3, 5, 4, 13, 12, 5, 25, 61, 28, 6, 42, 190, 256, 66, 7, 65, 526, 1372, 1117, 156, 8, 95, 1262, 6527, 10405, 5012, 368, 9, 133, 2766, 27415, 86360, 83029, 22592, 868, 10, 180, 5647, 104291, 635873, 1225281, 685898, 102336, 2048, 11, 237, 10878, 363859
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OFFSET
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1,1
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COMMENTS
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Table starts
....2.......3.........4...........5............6............7............8
....5......13........25..........42...........65...........95..........133
...12......61.......190.........526.........1262.........2766.........5647
...28.....256......1372........6527........27415.......104291.......363859
...66....1117.....10405.......86360.......635873......4267171.....26152051
..156....5012.....83029.....1225281.....15981219....191691132...2090236137
..368...22592....685898....18392485....429788876...9314138750.182333502325
..868..102336...5825700...290513038..12392346376.491124025940
.2048..465662..50417154..4767970186.378942837634
.4832.2123857.441675344.80410934960
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1) +2*a(n-3)
k=2: [order 26]
Empirical for row n:
n=1: a(n) = n + 1
n=2: a(n) = (1/6)*n^3 + 1*n^2 + (23/6)*n
n=3: [polynomial of degree 8] for n>6
n=4: [polynomial of degree 19] for n>20
n=5: [polynomial of degree 44] for n>52
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EXAMPLE
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Some solutions for n=4 k=4
..0..3..3..0....0..0..3..3....3..3..0..0....3..3..0..0....0..0..0..0
..0..0..2..1....0..3..2..3....2..2..3..3....0..3..1..3....3..3..0..0
..3..3..0..0....0..0..2..2....2..0..0..0....3..3..1..2....3..3..1..3
..2..1..2..0....0..3..2..3....3..1..0..0....2..2..2..1....3..3..2..2
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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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