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A279268 T(n,k)=Number of nXk 0..1 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. 7
0, 0, 0, 2, 4, 2, 2, 10, 10, 2, 5, 20, 29, 20, 5, 8, 38, 86, 86, 38, 8, 15, 68, 240, 400, 240, 68, 15, 26, 120, 626, 1592, 1592, 626, 120, 26, 46, 208, 1603, 5888, 9042, 5888, 1603, 208, 46, 80, 358, 4030, 21882, 51568, 51568, 21882, 4030, 358, 80, 139, 612, 9973, 79112 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Table starts

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

..0...4....10.....20.......38.........68.........120...........208

..2..10....29.....86......240........626........1603..........4030

..2..20....86....400.....1592.......5888.......21882.........79112

..5..38...240...1592.....9042......51568......283450.......1526492

..8..68...626...5888....51568.....429716.....3490152......27850092

.15.120..1603..21882...283450....3490152....42093113.....498160278

.26.208..4030..79112..1526492...27850092...498160278....8746623144

.46.358..9973.281754..8110769..218952412..5812405127..151499712450

.80.612.24388.991292.42557410.1701805320.67071788240.2595668095672

LINKS

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

FORMULA

Empirical for column k:

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

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>9

k=4: [order 28] for n>31

k=5: [order 58] for n>69

EXAMPLE

Some solutions for n=4 k=4

..0..1..1..0. .0..0..1..1. .0..1..1..1. .0..1..0..0. .0..1..0..1

..1..0..0..1. .1..1..0..1. .1..0..1..0. .1..1..1..1. .0..0..1..0

..0..1..0..1. .0..0..1..0. .0..0..1..1. .0..1..0..0. .1..0..1..0

..0..1..1..0. .1..0..1..0. .1..1..0..0. .0..1..0..1. .0..1..0..1

CROSSREFS

Column 1 is A006367(n-1).

Sequence in context: A278540 A280161 A280124 * A279856 A054507 A182742

Adjacent sequences:  A279265 A279266 A279267 * A279269 A279270 A279271

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 08 2016

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)