A275565 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,0) (-1,2) or (0,-2) and new values introduced in order 0..2.

1, 2, 2, 3, 14, 3, 6, 36, 54, 6, 12, 96, 126, 216, 12, 24, 288, 294, 504, 864, 24, 48, 864, 672, 1176, 1872, 3456, 48, 96, 2592, 1536, 3192, 4056, 7200, 13824, 96, 192, 7776, 3552, 8664, 13104, 15000, 27360, 55296, 192, 384, 23328, 8214, 23712, 42336, 57600

Offset

1,2

Comments

Table starts

...1......2.......3.......6.......12........24.........48..........96

...2.....14......36......96......288.......864.......2592........7776

...3.....54.....126.....294......672......1536.......3552........8214

...6....216.....504....1176.....3192......8664......23712.......64896

..12....864....1872....4056....13104.....42336.....138600......453750

..24...3456....7200...15000....57600....221184.....867456.....3402054

..48..13824...27360...54150...248520...1140576....5360184....25190406

..96..55296..104256..196566..1075140...5880600...33275880...188294424

.192.221184..397440..714150..4663710..30456054..206892990..1405458150

.384.884736.1513728.2589894.20186982.157347846.1286374716.10516571736

Links

R. H. Hardin, Table of n, a(n) for n = 1..286

Formula

Empirical for column k:

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

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

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

k=4: [order 10] for n>11

k=5: [order 32] for n>34

k=6: [order 35] for n>37

Empirical for row n:

n=1: a(n) = 2*a(n-1) for n>3

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

n=3: a(n) = 3*a(n-1) -5*a(n-3) +a(n-4) +7*a(n-5) -5*a(n-6) +2*a(n-8) -a(n-9) for n>10

n=4: [order 25] for n>28

n=5: [order 63] for n>66

Example

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

Crossrefs

Column 1 is A003945(n-2).

Column 2 is A208428.

Row 1 is A003945(n-2).

Sequence in context: A073828 A338523 A189312 * A275090 A274983 A153938

Adjacent sequences: A275562 A275563 A275564 * A275566 A275567 A275568

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 01 2016

Status

approved