A282189 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than four of its king-move neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 8, 44, 8, 0, 0, 104, 2919, 2919, 104, 0, 0, 1222, 122866, 418178, 122866, 1222, 0, 0, 13552, 4446172, 48031921, 48031921, 4446172, 13552, 0, 0, 144784, 148868304, 4907541118, 15775532484, 4907541118, 148868304, 144784, 0

Offset

1,12

Comments

Table starts

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

.0........0............1..............8..............104.............1222

.0........1...........44...........2919...........122866..........4446172

.0........8.........2919.........418178.........48031921.......4907541118

.0......104.......122866.......48031921......15775532484....4628006363340

.0.....1222......4446172.....4907541118....4628006363340.3903552450233444

.0....13552....148868304...469203486998.1272857909584052

.0...144784...4745726158.42928015621172

.0..1506870.146320129628

.0.15382464

Links

R. H. Hardin, Table of n, a(n) for n = 1..71

Formula

Empirical for column k:

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

k=2: a(n) = 16*a(n-1) -48*a(n-2) -116*a(n-3) -160*a(n-4) -96*a(n-5) -36*a(n-6) for n>9

k=3: [order 30] for n>33

Example

Some solutions for n=3 k=4
..0..1..0..0. .0..1..1..0. .0..1..0..0. .0..0..1..0. .0..1..1..1
..2..0..0..1. .1..2..2..2. .1..2..0..0. .0..0..0..1. .0..1..1..2
..0..2..0..0. .1..2..2..2. .1..2..0..0. .1..0..1..0. .1..1..0..0

Crossrefs

Sequence in context: A199321 A346198 A144039 * A210125 A044110 A044491

Adjacent sequences: A282186 A282187 A282188 * A282190 A282191 A282192

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 08 2017

Status

approved