A283347 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than two of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element.

0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 26, 71, 26, 0, 0, 120, 572, 572, 120, 0, 0, 524, 4398, 7804, 4398, 524, 0, 0, 2174, 31952, 106310, 106310, 31952, 2174, 0, 0, 8816, 224927, 1354928, 2519010, 1354928, 224927, 8816, 0, 0, 35036, 1546856, 16714556, 55886238

Offset

1,8

Comments

Table starts

.0.....0........0..........0............0...............0.................0

.0.....0........6.........26..........120.............524..............2174

.0.....6.......71........572.........4398...........31952............224927

.0....26......572.......7804.......106310.........1354928..........16714556

.0...120.....4398.....106310......2519010........55886238........1199035122

.0...524....31952....1354928.....55886238......2154364298.......80410575348

.0..2174...224927...16714556...1199035122.....80410575348.....5221636463228

.0..8816..1546856..201420678..25121756412...2929763437610...330934422791290

.0.35036.10453311.2383832160.516765464924.104800502322828.20589913083547464

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: [order 16]

k=3: [order 16]

k=4: [order 38]

Example

Some solutions for n=4 k=4
..0..1..0..0. .1..1..1..0. .0..0..0..1. .1..1..1..0. .0..1..0..1
..0..0..0..0. .1..0..1..0. .0..1..0..0. .1..0..0..0. .1..0..0..0
..1..1..0..1. .0..0..0..1. .1..1..1..0. .0..1..0..1. .1..1..0..0
..0..1..1..1. .0..0..1..0. .0..0..0..1. .0..1..1..0. .1..0..0..0

Crossrefs

Sequence in context: A002892 A055667 A281080 * A334710 A283203 A155742

Adjacent sequences: A283344 A283345 A283346 * A283348 A283349 A283350

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 05 2017

Status

approved