A279925 T(n,k)=Number of nXk 0..2 arrays with no element equal 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, 0, 0, 3, 15, 15, 3, 6, 142, 474, 142, 6, 24, 1350, 14281, 14281, 1350, 24, 72, 12858, 399487, 1230799, 399487, 12858, 72, 232, 119396, 11023893, 99427182, 99427182, 11023893, 119396, 232, 720, 1095012, 295670293, 7837914954

Offset

1,7

Comments

Table starts

....0........1............0..............3................6...............24

....1........0...........15............142.............1350............12858

....0.......15..........474..........14281...........399487.........11023893

....3......142........14281........1230799.........99427182.......7837914954

....6.....1350.......399487.......99427182......23145488444....5222809114196

...24....12858.....11023893.....7837914954....5222809114196.3362092868045434

...72...119396....295670293...601248781220.1145113368668739

..232..1095012...7789959515.45231133438998

..720..9924024.202165948916

.2232.89076240

Links

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

Formula

Empirical for column k:

k=1: a(n) = 6*a(n-1) -6*a(n-2) -16*a(n-3) +12*a(n-4) +24*a(n-5) +8*a(n-6) for n>8

k=2: [order 18] for n>19

k=3: [order 54] for n>58

Example

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

Crossrefs

Column 1 is A279300.

Sequence in context: A063628 A280201 A296842 * A279534 A181404 A096672

Adjacent sequences: A279922 A279923 A279924 * A279926 A279927 A279928

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 23 2016

Status

approved