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A279527
T(n,k)=Number of nXk 0..2 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
5
0, 0, 0, 2, 4, 2, 4, 46, 46, 4, 14, 384, 1168, 384, 14, 40, 2894, 23610, 23610, 2894, 40, 120, 20444, 456846, 1280440, 456846, 20444, 120, 352, 138944, 8451524, 66239560, 66239560, 8451524, 138944, 352, 1032, 918744, 152161078, 3300066400, 9202124094
OFFSET
1,4
COMMENTS
Table starts
....0.......0...........2...............4................14.................40
....0.......4..........46.............384..............2894..............20444
....2......46........1168...........23610............456846............8451524
....4.....384.......23610.........1280440..........66239560.........3300066400
...14....2894......456846........66239560........9202124094......1236882205974
...40...20444.....8451524......3300066400.....1236882205974....449916256454948
..120..138944...152161078....160408991208...162587780938059.160287240382480502
..352..918744..2683339202...7651924962192.21008453040002014
.1032.5954690.46585256882.359787825135858
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4) for n>5
k=2: [order 8]
k=3: [order 22]
EXAMPLE
Some solutions for n=3 k=4
..0..1..1..0. .0..1..2..2. .0..1..2..2. .0..0..1..2. .0..1..2..0
..1..0..1..1. .1..0..0..0. .0..1..0..1. .2..2..0..2. .2..1..1..2
..2..2..0..2. .0..2..0..1. .1..2..0..0. .1..1..0..2. .2..1..2..1
CROSSREFS
Column 1 is A279322.
Sequence in context: A193378 A108445 A263424 * A347184 A019294 A238262
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 14 2016
STATUS
approved