A279494 T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal, vertical and antidiagonal 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, 5, 5, 3, 3, 18, 38, 18, 3, 9, 68, 254, 254, 68, 9, 15, 235, 1433, 2684, 1433, 235, 15, 31, 801, 8330, 26157, 26157, 8330, 801, 31, 57, 2678, 46095, 246237, 425588, 246237, 46095, 2678, 57, 108, 8777, 250440, 2241332, 6559816, 6559816

Offset

1,7

Comments

Table starts

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

...1.....0.......5.........18...........68............235..............801

...0.....5......38........254.........1433...........8330............46095

...3....18.....254.......2684........26157.........246237..........2241332

...3....68....1433......26157.......425588........6559816.........98128162

...9...235....8330.....246237......6559816......166229033.......4065077852

..15...801...46095....2241332.....98128162.....4065077852.....162346342126

..31..2678..250440...19885341...1427793365....96674459373....6294925767121

..57..8777.1332366..172968364..20331614084..2247110811000..238434528280477

.108.28343.6989712.1481176019.284582186755.51300573165630.8863487201716422

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 16]

k=3: [order 54] for n>55

Example

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

Crossrefs

Column 1 is A105423(n-2).

Sequence in context: A199614 A129488 A211023 * A053670 A085963 A282177

Adjacent sequences: A279491 A279492 A279493 * A279495 A279496 A279497

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 13 2016

Status

approved