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A280313
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T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
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5
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0, 0, 0, 0, 0, 0, 1, 15, 15, 1, 2, 222, 788, 222, 2, 9, 2348, 20274, 20274, 2348, 9, 34, 21302, 415198, 1047790, 415198, 21302, 34, 124, 176125, 7506237, 43973846, 43973846, 7506237, 176125, 124, 432, 1370378, 125467047, 1638451216, 3802506340
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OFFSET
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1,8
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COMMENTS
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Table starts
....0........0............0..............1................2................9
....0........0...........15............222.............2348............21302
....0.......15..........788..........20274...........415198..........7506237
....1......222........20274........1047790.........43973846.......1638451216
....2.....2348.......415198.......43973846.......3802506340.....292789164101
....9....21302......7506237.....1638451216.....292789164101...46670265882656
...34...176125....125467047....56602534187...20928606452792.6910403433332994
..124..1370378...1986983748..1855013487412.1420117779715304
..432.10206549..30245976536.58477471703834
.1464.73563740.446674283782
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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) -6*a(n-2) -16*a(n-3) +12*a(n-4) +24*a(n-5) +8*a(n-6) for n>10
k=2: [order 12]
k=3: [order 36] for n>38
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EXAMPLE
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Some solutions for n=3 k=4
..0..0..1..2. .0..1..2..1. .0..0..1..1. .0..1..0..2. .0..0..0..1
..1..0..2..0. .2..1..2..0. .2..0..2..2. .1..1..0..1. .2..2..2..1
..2..0..2..0. .0..2..2..2. .2..2..1..0. .0..2..0..1. .1..1..0..0
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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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