A279580 T(n,k)=Number of nXk 0..2 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 2, 4, 0, 4, 36, 40, 0, 14, 304, 944, 352, 0, 40, 2212, 20776, 23072, 3008, 0, 120, 15428, 406200, 1356120, 547168, 25280, 0, 352, 103648, 7630156, 72177144, 86246944, 12701248, 209792, 0, 1032, 680052, 138602548, 3684310576, 12490527012

Offset

1,4

Comments

Table starts

.0.......0..........2..............4................14....................40

.0.......4.........36............304..............2212.................15428

.0......40........944..........20776............406200...............7630156

.0.....352......23072........1356120..........72177144............3684310576

.0....3008.....547168.......86246944.......12490527012.........1732429706176

.0...25280...12701248.....5385546376.....2121871518232.......800037452999320

.0..209792..290067328...331573929104...355347019237332....364333887872124232

.0.1723392.6540226304.20185283466808.58835479020749472.164074884296083732404

Links

R. H. Hardin, Table of n, a(n) for n = 1..110

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 16*a(n-1) -72*a(n-2) +64*a(n-3) -16*a(n-4)

k=3: [order 6] for n>7

k=4: [order 16] for n>17

k=5: [order 28] for n>29

Empirical for row n:

n=1: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4) for n>5

n=2: [order 8]

n=3: [order 34] for n>35

Example

Some solutions for n=3 k=4
..0..0..1..0. .0..1..1..1. .0..1..1..2. .0..1..2..1. .0..1..2..1
..1..2..1..2. .2..0..0..0. .1..0..0..2. .0..2..2..2. .1..0..0..2
..0..1..0..2. .0..2..2..0. .2..0..2..1. .1..2..1..0. .0..2..2..1

Crossrefs

Row 1 is A279322.

Sequence in context: A059226 A221655 A221087 * A197513 A097666 A144810

Adjacent sequences: A279577 A279578 A279579 * A279581 A279582 A279583

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 15 2016

Status

approved