A281765 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 2, 4, 0, 2, 14, 10, 0, 5, 40, 47, 20, 0, 8, 110, 152, 90, 38, 0, 15, 280, 609, 560, 201, 68, 0, 26, 698, 2138, 2808, 1872, 374, 120, 0, 46, 1696, 7466, 13968, 12191, 5948, 672, 208, 0, 80, 4052, 25798, 68362, 85844, 49986, 18358, 1172, 358, 0, 139, 9564, 87397

Offset

1,4

Comments

Table starts

.0...0....2......2........5.........8..........15...........26.............46

.0...4...14.....40......110.......280.........698.........1696...........4052

.0..10...47....152......609......2138........7466........25798..........87397

.0..20...90....560.....2808.....13968.......68362.......323280........1529974

.0..38..201...1872....12191.....85844......589990......3845590.......25703392

.0..68..374...5948....49986....502276.....4845178.....43943360......414035752

.0.120..672..18358...201450...2848436....38998648....491290688.....6531040026

.0.208.1172..55048...795220..15817652...306847534...5380228500...100838834642

.0.358.2015.162120..3098932..86332266..2376142873..58064622712..1533079336619

.0.612.3442.471340.11944444.465260812.18172170592.619082149716.23019093115418

Links

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

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

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>11

k=4: [order 29] for n>32

k=5: [order 48] for n>57

Empirical for row n:

n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) for n>5

n=2: [order 9]

n=3: [order 40] for n>41

Example

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

Crossrefs

Column 2 is A279262.

Row 1 is A006367(n-1).

Sequence in context: A153182 A111818 A007631 * A155517 A325490 A123514

Adjacent sequences: A281762 A281763 A281764 * A281766 A281767 A281768

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 29 2017

Status

approved