A279134 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 two elements, and with new values introduced in order 0 sequentially upwards.

0, 1, 1, 0, 0, 0, 3, 9, 9, 3, 3, 34, 66, 34, 3, 9, 87, 256, 256, 87, 9, 15, 194, 820, 1324, 820, 194, 15, 31, 400, 2551, 6396, 6396, 2551, 400, 31, 57, 790, 7491, 30074, 47452, 30074, 7491, 790, 57, 108, 1511, 21131, 129264, 316516, 316516, 129264, 21131, 1511, 108

Offset: 1

Author

R. H. Hardin, Dec 06 2016

Keywords

• nonn
• tabl

Comments

Table starts

...0....1......0.......3.........3...........9...........15.............31

...1....0......9......34........87.........194..........400............790

...0....9.....66.....256.......820........2551.........7491..........21131

...3...34....256....1324......6396.......30074.......129264.........535814

...3...87....820....6396.....47452......316516......2017028.......12376570

...9..194...2551...30074....316516.....3125600.....29410145......266502710

..15..400...7491..129264...2017028....29410145....409061044.....5488392521

..31..790..21131..535814..12376570...266502710...5488392521...109117856920

..57.1511..57971.2150797..73672888..2346800921..71618045798..2111166039927

.108.2830.155551.8418336.428568648.20197483932.913912909445.39962431131266

Examples

			Some solutions for n=4 k=4
..0..0..1..0. .0..0..0..1. .0..1..0..1. .0..1..0..1. .0..0..1..0
..1..0..1..1. .1..1..1..0. .0..0..1..0. .1..0..1..0. .1..1..0..1
..1..1..0..0. .0..0..0..1. .0..1..0..0. .0..1..1..0. .1..0..1..0
..1..0..1..1. .1..0..1..0. .1..0..1..0. .0..1..0..0. .0..0..0..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 8] for n>9

k=3: [order 11] for n>17

k=4: [order 43] for n>50

k=5: [order 88] for n>108