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.

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

R. H. Hardin, Table of n, a(n) for n = 1..313

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

Adjacent sequences: A281397 A281398 A281399 * A281401 A281402 A281403

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 21 2017

Status

approved