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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.
8
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 11 2016
STATUS
approved