A279384 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 new values introduced in order 0 sequentially upwards.

1, 1, 1, 1, 3, 1, 2, 8, 8, 2, 3, 22, 35, 22, 3, 5, 61, 157, 157, 61, 5, 8, 170, 695, 1101, 695, 170, 8, 13, 472, 3157, 7905, 7905, 3157, 472, 13, 21, 1310, 14243, 58009, 92803, 58009, 14243, 1310, 21, 34, 3637, 64170, 421999, 1098640, 1098640, 421999, 64170, 3637, 34

Offset

1,5

Comments

Table starts

..1.....1.......1.........2...........3.............5...............8

..1.....3.......8........22..........61...........170.............472

..1.....8......35.......157.........695..........3157...........14243

..2....22.....157......1101........7905.........58009..........421999

..3....61.....695......7905.......92803.......1098640........12957948

..5...170....3157.....58009.....1098640......21144799.......404651396

..8...472...14243....421999....12957948.....404651396.....12564378389

.13..1310...64170...3067328...152622739....7733370493....389417147928

.21..3637..289200..22304530..1798168331..147824883279..12073180118618

.34.10099.1303737.162224094.21189754515.2826526873740.374420804035101

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2) for n>3

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

k=3: [order 18]

k=4: [order 57] for n>58

Example

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

Crossrefs

Column 1 is A000045(n-1).

Sequence in context: A272536 A204122 A201657 * A086961 A204003 A085194

Adjacent sequences: A279381 A279382 A279383 * A279385 A279386 A279387

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 11 2016

Status

approved