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

Author

R. H. Hardin, Dec 12 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A006367(n-1).

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]