A281765 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 2, 4, 0, 2, 14, 10, 0, 5, 40, 47, 20, 0, 8, 110, 152, 90, 38, 0, 15, 280, 609, 560, 201, 68, 0, 26, 698, 2138, 2808, 1872, 374, 120, 0, 46, 1696, 7466, 13968, 12191, 5948, 672, 208, 0, 80, 4052, 25798, 68362, 85844, 49986, 18358, 1172, 358, 0, 139, 9564, 87397

Offset: 1

Author

R. H. Hardin, Jan 29 2017

Keywords

• nonn
• tabl

Comments

Table starts

.0...0....2......2........5.........8..........15...........26.............46

.0...4...14.....40......110.......280.........698.........1696...........4052

.0..10...47....152......609......2138........7466........25798..........87397

.0..20...90....560.....2808.....13968.......68362.......323280........1529974

.0..38..201...1872....12191.....85844......589990......3845590.......25703392

.0..68..374...5948....49986....502276.....4845178.....43943360......414035752

.0.120..672..18358...201450...2848436....38998648....491290688.....6531040026

.0.208.1172..55048...795220..15817652...306847534...5380228500...100838834642

.0.358.2015.162120..3098932..86332266..2376142873..58064622712..1533079336619

.0.612.3442.471340.11944444.465260812.18172170592.619082149716.23019093115418

Examples

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

Links

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

Crossrefs

Column 2 is A279262.

Row 1 is A006367(n-1).

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

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

k=3: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>11

k=4: [order 29] for n>32

k=5: [order 48] for n>57

Empirical for row n:

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

n=2: [order 9]

n=3: [order 40] for n>41