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

1,7

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

Links

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

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

Example

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

Crossrefs

Column 1 is A105423(n-2).

Sequence in context: A360178 A157349 A159811 * A083352 A243350 A091559

Adjacent sequences: A279131 A279132 A279133 * A279135 A279136 A279137

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 06 2016

Status

approved