A280217 T(n,k) = Number of n X k 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 1, 1, 0, 2, 0, 6, 26, 26, 6, 6, 92, 158, 92, 6, 30, 307, 886, 886, 307, 30, 54, 1072, 4382, 7048, 4382, 1072, 54, 158, 3541, 20593, 49328, 49328, 20593, 3541, 158, 342, 11834, 93326, 320755, 474433, 320755, 93326, 11834, 342, 846, 38687, 410789, 2001079

Offset

1,5

Comments

Table starts

...0......1.......0.........6..........6.........30.........54........158

...1......2......26........92........307.......1072.......3541......11834

...0.....26.....158.......886.......4382......20593......93326.....410789

...6.....92.....886......7048......49328.....320755....2001079...12072893

...6....307....4382.....49328.....474433....4245153...36290440..298709773

..30...1072...20593....320755....4245153...51995541..607401930.6826834071

..54...3541...93326...2001079...36290440..607401930.9673911703

.158..11834..410789..12072893..298709773.6826834071

.342..38687.1768582..71202942.2400798535

.846.125380.7492763.412532945

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1) +3*a(n-2) -11*a(n-3) -6*a(n-4) +12*a(n-5) +8*a(n-6);

k=2: [order 10] for n>14;

k=3: [order 21] for n>28;

k=4: [order 42] for n>51.

Example

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

Crossrefs

Column 1 is A279865.

Sequence in context: A362685 A171734 A278746 * A079203 A151751 A196354

Adjacent sequences: A280214 A280215 A280216 * A280218 A280219 A280220

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 29 2016

Status

approved