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A275131
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T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.
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12
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1, 2, 1, 5, 4, 2, 14, 16, 12, 4, 41, 64, 45, 36, 8, 122, 256, 174, 129, 108, 16, 365, 1024, 675, 568, 373, 324, 32, 1094, 4096, 2607, 2545, 2178, 1083, 972, 64, 3281, 16384, 10077, 11092, 12423, 8321, 3148, 2916, 128, 9842, 65536, 38967, 48451, 71576, 62378
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OFFSET
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1,2
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COMMENTS
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Table starts
...1.....2.....5......14.......41.......122.........365.........1094
...1.....4....16......64......256......1024........4096........16384
...2....12....45.....174......675......2607.......10077........38967
...4....36...129.....568.....2545.....11092.......48451.......212897
...8...108...373....2178....12423.....71576......412306......2381629
..16...324..1083....8321....62378....473185.....3586068.....27224209
..32...972..3148...31772...315021...3146574....31446544....315531602
..64..2916..9157..121707..1591442..20970214...276145917...3669759648
.128..8748.26623..466252..8024937.139845553..2432426709..42807577389
.256.26244.77372.1783920.40445177.930732169.21443562178.499213473864
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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) for n>2
k=2: a(n) = 3*a(n-1) for n>2
k=3: [order 9] for n>10
k=4: [order 17] for n>20
k=5: [order 28] for n>31
k=6: [order 67] for n>70
Empirical for row n:
n=1: a(n) = 4*a(n-1) -3*a(n-2)
n=2: a(n) = 4*a(n-1)
n=3: a(n) = 3*a(n-1) +2*a(n-2) +6*a(n-3) -2*a(n-4) -4*a(n-5) for n>6
n=4: [order 9] for n>11
n=5: [order 10] for n>14
n=6: [order 26] for n>28
n=7: [order 53] for n>58
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..1..1. .0..0..1..1. .0..1..2..2. .0..1..1..1. .0..0..1..2
..2..2..0..2. .2..2..2..0. .2..0..1..0. .2..2..0..0. .1..2..0..1
..1..1..1..1. .0..0..1..2. .1..2..2..2. .1..1..1..2. .0..1..2..2
..0..0..0..0. .2..2..0..0. .0..1..1..1. .2..2..0..1. .2..0..0..1
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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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