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A281400
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.
14
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
OFFSET
1,8
COMMENTS
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
LINKS
FORMULA
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
EXAMPLE
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
CROSSREFS
Sequence in context: A239603 A241439 A276348 * A283726 A370388 A010171
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 21 2017
STATUS
approved