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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. 12
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 29 2017
STATUS
approved

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Last modified June 20 14:54 EDT 2024. Contains 373526 sequences. (Running on oeis4.)