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A281326
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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 antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
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11
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0, 0, 0, 1, 2, 0, 2, 46, 28, 0, 8, 394, 1266, 304, 0, 28, 3102, 21734, 27144, 2976, 0, 94, 22342, 350818, 953236, 521848, 27488, 0, 304, 153982, 5192104, 31906806, 37854870, 9439296, 244544, 0, 960, 1028164, 73653131, 977717308, 2628860468, 1420883314
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OFFSET
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1,5
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COMMENTS
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Table starts
.0.........0............1................2.................8.................28
.0.........2...........46..............394..............3102..............22342
.0........28.........1266............21734............350818............5192104
.0.......304........27144...........953236..........31906806..........977717308
.0......2976.......521848.........37854870........2628860468.......166805996158
.0.....27488......9439296.......1420883314......204635003232.....26899223667928
.0....244544....164206368......51413566384....15351923549506...4181821443113978
.0...2119168...2780073856....1813061036754..1122266386967854.633606104886468360
.0..18011136..46137121152...62727044483806.80481356765998482
.0.150809088.754039756800.2138467742923228
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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) = 16*a(n-1) -72*a(n-2) +64*a(n-3) -16*a(n-4)
k=3: a(n) = 28*a(n-1) -180*a(n-2) -224*a(n-3) -64*a(n-4) for n>5
k=4: [order 8] for n>9
k=5: [order 16] for n>18
Empirical for row n:
n=1: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4) for n>7
n=2: [order 10] for n>11
n=3: [order 36] for n>39
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EXAMPLE
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Some solutions for n=3 k=4
..0..1..2..2. .0..0..1..2. .0..1..2..1. .0..1..0..2. .0..1..2..1
..2..1..1..0. .1..0..1..1. .1..0..1..1. .0..0..2..0. .2..0..0..1
..2..1..2..2. .2..0..0..0. .0..1..2..0. .2..1..2..2. .2..0..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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