A279856 T(n,k)=Number of nXk 0..2 arrays with no element unequal 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.

0, 0, 0, 2, 4, 2, 2, 10, 10, 2, 8, 24, 49, 24, 8, 14, 54, 168, 168, 54, 14, 36, 116, 557, 972, 557, 116, 36, 74, 250, 1758, 5200, 5200, 1758, 250, 74, 168, 528, 5441, 26632, 44893, 26632, 5441, 528, 168, 358, 1118, 16500, 134898, 373516, 373516, 134898, 16500

Offset

1,4

Comments

Table starts

...0....0......2........2..........8..........14..........36..........74

...0....4.....10.......24.........54.........116.........250.........528

...2...10.....49......168........557........1758........5441.......16500

...2...24....168......972.......5200.......26632......134898......668668

...8...54....557.....5200......44893......373516.....3010179....23836450

..14..116...1758....26632.....373516.....4989784....64921744...827573664

..36..250...5441...134898....3010179....64921744..1356293555.27796618392

..74..528..16500...668668...23836450...827573664.27796618392

.168.1118..49253..3278294..185854745.10392951988

.358.2348.145290.15902088.1432781380

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +a(n-2) -7*a(n-3) +4*a(n-5)

k=3: a(n) = 4*a(n-1) -2*a(n-2) -9*a(n-4) -4*a(n-5) -4*a(n-6) for n>9

k=4: [order 38] for n>41

Example

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

Crossrefs

Column 1 is A219754(n+1)*2.

Sequence in context: A280161 A280124 A279268 * A054507 A182742 A087229

Adjacent sequences: A279853 A279854 A279855 * A279857 A279858 A279859

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 20 2016

Status

approved