A279494 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 two elements, and with new values introduced in order 0 sequentially upwards.

0, 1, 1, 0, 0, 0, 3, 5, 5, 3, 3, 18, 38, 18, 3, 9, 68, 254, 254, 68, 9, 15, 235, 1433, 2684, 1433, 235, 15, 31, 801, 8330, 26157, 26157, 8330, 801, 31, 57, 2678, 46095, 246237, 425588, 246237, 46095, 2678, 57, 108, 8777, 250440, 2241332, 6559816, 6559816

Offset: 1

Author

R. H. Hardin, Dec 13 2016

Keywords

• nonn
• tabl

Comments

Table starts

...0.....1.......0..........3............3..............9...............15

...1.....0.......5.........18...........68............235..............801

...0.....5......38........254.........1433...........8330............46095

...3....18.....254.......2684........26157.........246237..........2241332

...3....68....1433......26157.......425588........6559816.........98128162

...9...235....8330.....246237......6559816......166229033.......4065077852

..15...801...46095....2241332.....98128162.....4065077852.....162346342126

..31..2678..250440...19885341...1427793365....96674459373....6294925767121

..57..8777.1332366..172968364..20331614084..2247110811000..238434528280477

.108.28343.6989712.1481176019.284582186755.51300573165630.8863487201716422

Examples

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

Links

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

Crossrefs

Column 1 is A105423(n-2).

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1) -5*a(n-3) +3*a(n-5) +a(n-6)

k=2: [order 16]

k=3: [order 54] for n>55