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A269035
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T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.
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13
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0, 3, 0, 12, 24, 0, 36, 48, 120, 0, 96, 216, 348, 504, 0, 240, 672, 2166, 2136, 1944, 0, 576, 2208, 9528, 18384, 12228, 7128, 0, 1344, 6912, 44760, 115656, 146064, 67104, 25272, 0, 3072, 21408, 198816, 785124, 1326576, 1114848, 357756, 87480, 0, 6912, 65280
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OFFSET
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1,2
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COMMENTS
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Table starts
.0......3.......12.........36...........96............240.............576
.0.....24.......48........216..........672...........2208............6912
.0....120......348.......2166.........9528..........44760..........198816
.0....504.....2136......18384.......115656.........785124.........4998648
.0...1944....12228.....146064......1326576.......13031664.......119790816
.0...7128....67104....1114848.....14710368......208867428......2783857776
.0..25272...357756....8277072....159397596.....3266423688.....63310818360
.0..87480..1867560...60218112...1698064656....50155587360...1416701634552
.0.297432..9593844..431354928..17853542544...759280601376..31304407671636
.0.997272.48665904.3052215072.185754411168.11364951702132.684763778434512
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 6*a(n-1) -9*a(n-2) for n>3
k=3: a(n) = 10*a(n-1) -29*a(n-2) +20*a(n-3) -4*a(n-4) for n>5
k=4: a(n) = 14*a(n-1) -57*a(n-2) +56*a(n-3) -16*a(n-4) for n>5
k=5: [order 12] for n>13
k=6: [order 18] for n>19
k=7: [order 38] for n>39
Empirical for row n:
n=1: a(n) = 4*a(n-1) -4*a(n-2)
n=2: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4)
n=3: a(n) = 6*a(n-1) -a(n-2) -28*a(n-3) -4*a(n-4) +16*a(n-5) -4*a(n-6) for n>8
n=4: [order 12] for n>14
n=5: [order 20] for n>22
n=6: [order 46] for n>48
n=7: [order 92] for n>94
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EXAMPLE
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Some solutions for n=4 k=4
..2..1..0..0. .0..0..1..0. .0..1..0..1. .2..0..0..1. .2..2..2..1
..0..1..0..0. .0..1..0..0. .0..0..0..1. .0..1..0..1. .1..2..2..2
..2..1..0..1. .0..1..0..0. .2..1..0..1. .2..1..0..1. .2..2..2..2
..0..0..0..0. .0..1..0..1. .0..1..0..1. .0..1..0..0. .1..1..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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