A279871 T(n,k)=Number of nXk 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 1, 1, 0, 4, 0, 6, 33, 33, 6, 6, 96, 176, 96, 6, 30, 255, 824, 824, 255, 30, 54, 610, 3199, 5704, 3199, 610, 54, 158, 1437, 11983, 37289, 37289, 11983, 1437, 158, 342, 3292, 42296, 226118, 389786, 226118, 42296, 3292, 342, 846, 7451, 143968, 1300184

Offset

1,5

Comments

Table starts

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

...1.....4......33........96........255.........610........1437........3292

...0....33.....176.......824.......3199.......11983.......42296......143968

...6....96.....824......5704......37289......226118.....1300184.....7247300

...6...255....3199.....37289.....389786.....3786373....35086917...313383975

..30...610...11983....226118....3786373....59485548...887774030.12785911872

..54..1437...42296...1300184...35086917...887774030.21336315188

.158..3292..143968...7247300..313383975.12785911872

.342..7451..476675..39307590.2722202345

.846.16662.1543667.208922598

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 8] for n>9

k=3: [order 12] for n>18

k=4: [order 57] for n>64

Example

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

Crossrefs

Sequence in context: A222889 A223114 A222832 * A223052 A027857 A366408

Adjacent sequences: A279868 A279869 A279870 * A279872 A279873 A279874

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 21 2016

Status

approved