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A269194
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T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three no more than once.
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8
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4, 16, 16, 60, 108, 60, 216, 708, 708, 216, 756, 4476, 9284, 4476, 756, 2592, 27684, 115452, 115452, 27684, 2592, 8748, 168252, 1399612, 2817548, 1399612, 168252, 8748, 29160, 1008804, 16629436, 67134380, 67134380, 16629436, 1008804, 29160
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OFFSET
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1,1
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COMMENTS
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Table starts
......4........16...........60.............216................756
.....16.......108..........708............4476..............27684
.....60.......708.........9284..........115452............1399612
....216......4476.......115452.........2817548...........67134380
....756.....27684......1399612........67134380.........3159954052
...2592....168252.....16629436......1567933676.......145995171708
...8748...1008804....194596516.....36068275268......6648192704604
..29160...5983164...2249848972....819789099172....299224791093196
..96228..35170980..25758552060..18452018423420..13339889117822420
.314928.205214268.292530733516.411983259384452.590022908205332548
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 6*a(n-1) -9*a(n-2)
k=2: a(n) = 10*a(n-1) -21*a(n-2) -20*a(n-3) -4*a(n-4) for n>5
k=3: [order 8] for n>9
k=4: [order 16] for n>17
k=5: [order 40] for n>41
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EXAMPLE
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Some solutions for n=3 k=4
..0..1..1..3. .0..0..2..2. .2..3..1..3. .1..3..1..1. .2..3..2..1
..0..1..3..1. .2..0..0..2. .2..3..1..3. .1..1..1..3. .2..2..3..3
..1..3..1..1. .2..0..2..0. .3..3..1..0. .0..3..1..3. .3..2..3..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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