A279268 T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 2, 4, 2, 2, 10, 10, 2, 5, 20, 29, 20, 5, 8, 38, 86, 86, 38, 8, 15, 68, 240, 400, 240, 68, 15, 26, 120, 626, 1592, 1592, 626, 120, 26, 46, 208, 1603, 5888, 9042, 5888, 1603, 208, 46, 80, 358, 4030, 21882, 51568, 51568, 21882, 4030, 358, 80, 139, 612, 9973, 79112

Offset: 1

Author

R. H. Hardin, Dec 08 2016

Keywords

• nonn
• tabl

Comments

Table starts

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

..0...4....10.....20.......38.........68.........120...........208

..2..10....29.....86......240........626........1603..........4030

..2..20....86....400.....1592.......5888.......21882.........79112

..5..38...240...1592.....9042......51568......283450.......1526492

..8..68...626...5888....51568.....429716.....3490152......27850092

.15.120..1603..21882...283450....3490152....42093113.....498160278

.26.208..4030..79112..1526492...27850092...498160278....8746623144

.46.358..9973.281754..8110769..218952412..5812405127..151499712450

.80.612.24388.991292.42557410.1701805320.67071788240.2595668095672

Examples

			Some solutions for n=4 k=4
..0..1..1..0. .0..0..1..1. .0..1..1..1. .0..1..0..0. .0..1..0..1
..1..0..0..1. .1..1..0..1. .1..0..1..0. .1..1..1..1. .0..0..1..0
..0..1..0..1. .0..0..1..0. .0..0..1..1. .0..1..0..0. .1..0..1..0
..0..1..1..0. .1..0..1..0. .1..1..0..0. .0..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: 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>9

k=4: [order 28] for n>31

k=5: [order 58] for n>69