A279168 T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its king-move 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, 0, 0, 3, 3, 8, 16, 8, 3, 9, 24, 117, 117, 24, 9, 15, 88, 483, 864, 483, 88, 15, 31, 284, 2001, 5628, 5628, 2001, 284, 31, 57, 772, 7709, 34764, 57248, 34764, 7709, 772, 57, 108, 2000, 28139, 203226, 557163, 557163, 203226, 28139, 2000, 108, 199

Offset

1,7

Comments

Table starts

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

...1....0......0........8.........24...........88............284

...0....0.....16......117........483.........2001...........7709

...3....8....117......864.......5628........34764.........203226

...3...24....483.....5628......57248.......557163........5159514

...9...88...2001....34764.....557163......8426362......121098448

..15..284...7709...203226....5159514....121098448.....2708250146

..31..772..28139..1143396...45915548...1686053298....58954576326

..57.2000..99519..6219491..396958758..22825771952..1248383818884

.108.5008.343156.33013384.3354431037.302051174586.25842455526113

Links

R. H. Hardin, Table of n, a(n) for n = 1..161

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 11]

k=3: [order 33] for n>36

k=4: [order 84] for n>88

Example

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

Crossrefs

Column 1 is A105423(n-2).

Sequence in context: A282499 A216194 A365462 * A111787 A200524 A308223

Adjacent sequences: A279165 A279166 A279167 * A279169 A279170 A279171

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 07 2016

Status

approved