A280398 T(n,k) = Number of n X k 0..2 arrays with no element unequal 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, 2, 0, 2, 6, 14, 0, 8, 16, 66, 74, 0, 14, 34, 238, 554, 358, 0, 36, 76, 769, 3002, 4250, 1666, 0, 74, 158, 2432, 15476, 35676, 31242, 7582, 0, 168, 336, 7440, 78540, 292622, 410670, 223706, 33978, 0, 358, 698, 22494, 388686, 2366358, 5338004

Offset

1,4

Comments

Table starts

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

.0......2........6.........16...........34............76...........158

.0.....14.......66........238..........769..........2432..........7440

.0.....74......554.......3002........15476.........78540........388686

.0....358.....4250......35676.......292622.......2366358......18736311

.0...1666....31242.....410670......5338004......68842232.....874372050

.0...7582...223706....4627308.....95102542....1958524652...39877186802

.0..33978..1571978...51310794...1664838008...54763698930.1785907191220

.0.150486.10887706..561854184..28747146050.1510604213832

.0.660210.74545802.6090082758.490958066148

Links

R. H. Hardin, Table of n, a(n) for n = 1..111

Formula

Empirical for column k:

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

k=2: a(n) = 10*a(n-1) -33*a(n-2) +40*a(n-3) -16*a(n-4);

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

k=4: [order 14] for n>15;

k=5: [order 24] for n>25;

k=6: [order 64] for n>65.

Empirical for row n:

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

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

n=3: [order 17] for n>19;

n=4: [order 54] for n>59.

Example

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

Crossrefs

Sequence in context: A021458 A279741 A099064 * A052422 A294525 A011218

Adjacent sequences: A280395 A280396 A280397 * A280399 A280400 A280401

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 02 2017

Status

approved