A279466 T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 2, 2, 2, 2, 6, 6, 2, 5, 20, 33, 20, 5, 8, 66, 180, 180, 66, 8, 15, 210, 1024, 1722, 1024, 210, 15, 26, 658, 5228, 15484, 15484, 5228, 658, 26, 46, 2036, 26670, 129914, 223261, 129914, 26670, 2036, 46, 80, 6236, 134438, 1079792, 3086910, 3086910

Offset

1,4

Comments

Table starts

..0.....0.......2.........2...........5..............8...............15

..0.....2.......6........20..........66............210..............658

..2.....6......33.......180........1024...........5228............26670

..2....20.....180......1722.......15484.........129914..........1079792

..5....66....1024.....15484......223261........3086910.........41706415

..8...210....5228....129914.....3086910.......69493918.......1529974962

.15...658...26670...1079792....41706415.....1529974962......54755104784

.26..2036..134438...8845592...555052466....33126514762....1926654903560

.46..6236..670407..71540206..7290902341...707716447612...66854006751350

.80.18928.3310176.572555634.94741575142.14949807134092.2293311539588776

Links

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

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) for n>5

k=2: [order 10]

k=3: [order 36]

Example

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

Crossrefs

Column 1 is A006367(n-1).

Sequence in context: A238413 A151704 A110023 * A116863 A136494 A260188

Adjacent sequences: A279463 A279464 A279465 * A279467 A279468 A279469

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 12 2016

Status

approved