A279534 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 two elements, and with new values introduced in order 0 sequentially upwards.

0, 1, 1, 0, 0, 0, 3, 15, 15, 3, 6, 222, 668, 222, 6, 24, 2348, 21430, 21430, 2348, 24, 72, 21302, 539596, 1585524, 539596, 21302, 72, 232, 176125, 12335295, 102868091, 102868091, 12335295, 176125, 232, 720, 1370378, 263171408, 6167352480

Offset

1,7

Comments

Table starts

....0........1............0..............3...............6...............24

....1........0...........15............222............2348............21302

....0.......15..........668..........21430..........539596.........12335295

....3......222........21430........1585524.......102868091.......6167352480

....6.....2348.......539596......102868091.....17596660798....2810209481878

...24....21302.....12335295.....6167352480...2810209481878.1203474431523240

...72...176125....263171408...349780411336.427316604639150

..232..1370378...5359546513.19062177795838

..720.10206549.105415261452

.2232.73563740

Links

R. H. Hardin, Table of n, a(n) for n = 1..71

Formula

Empirical for column k:

k=1: a(n) = 6*a(n-1) -6*a(n-2) -16*a(n-3) +12*a(n-4) +24*a(n-5) +8*a(n-6) for n>8

k=2: [order 12] for n>13

k=3: [order 33] for n>35

Example

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

Crossrefs

Column 1 is A279300.

Sequence in context: A280201 A296842 A279925 * A181404 A096672 A344565

Adjacent sequences: A279531 A279532 A279533 * A279535 A279536 A279537

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 14 2016

Status

approved