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A281400
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T(n,k)=Number of nXk 0..1 arrays with no element equal to more than two of its horizontal, diagonal or antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
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14
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0, 0, 0, 0, 0, 0, 0, 10, 6, 0, 0, 52, 131, 36, 0, 0, 170, 314, 438, 160, 0, 0, 484, 689, 1020, 1413, 676, 0, 0, 1296, 1294, 2146, 2886, 3838, 2692, 0, 0, 3308, 2364, 3736, 5892, 7064, 10226, 10352, 0, 0, 8222, 4338, 6276, 10130, 13446, 17194, 26468, 38868, 0, 0, 19996
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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......0......0......0......0.......0.......0.......0.......0
.0......0.....10.....52....170....484...1296....3308....8222...19996...47894
.0......6....131....314....689...1294...2364....4338....7850...14150...25510
.0.....36....438...1020...2146...3736...6276...10740...18472...31360...53204
.0....160...1413...2886...5892..10130..16241...25680...41353...67226..108849
.0....676...3838...7064..13446..23216..37462...57468...87252..135112..211998
.0...2692..10226..17194..30959..51940..84474..129934..192666..283820..424420
.0..10352..26468..42396..73600.117788.185834..285076..421646..607684..871772
.0..38868..66952.101410.169161.262870.400854..599826..886900.1278956.1803092
.0.143276.166702.239524.384546.583824.871302.1265460.1838934.2652496.3748502
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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) -7*a(n-2) -6*a(n-3) -5*a(n-4) +12*a(n-5) +4*a(n-6) -4*a(n-8)
k=3: [order 14] for n>19
k=4: [order 15] for n>21
k=5: [order 19] for n>30
k=6: [order 21] for n>34
k=7: [order 23] for n>38
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: [order 9] for n>10
n=3: [order 8] for n>13
n=4: [order 10] for n>16
n=5: [order 12] for n>19
n=6: [order 14] for n>25
n=7: [order 16] for n>31
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..1..0. .0..1..0..1
..1..0..1..0. .1..1..1..0. .0..1..0..1. .1..0..0..0. .1..0..1..0
..0..1..1..0. .1..0..1..0. .1..1..0..1. .1..0..1..1. .1..0..1..1
..0..0..1..0. .0..0..1..1. .1..0..0..0. .1..0..1..1. .0..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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