A230819 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 3 and at least one element with value (x(i,j)-1) mod 3, and upper left element zero.

0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 4, 0, 0, 0, 2, 12, 12, 2, 0, 0, 12, 100, 174, 100, 12, 0, 0, 18, 326, 816, 816, 326, 18, 0, 0, 56, 2114, 12210, 28772, 12210, 2114, 56, 0, 0, 170, 9226, 108006, 497166, 497166, 108006, 9226, 170, 0, 0, 420, 47220, 1202184, 10872238

Offset

1,8

Comments

Table starts

.0..0....0.......0.........0...........0.............0.............0

.0..0....2.......0.........2..........12............18............56

.0..2....4......12.......100.........326..........2114..........9226

.0..0...12.....174.......816.......12210........108006.......1202184

.0..2..100.....816.....28772......497166......10872238.....222626294

.0.12..326...12210....497166....21835516.....888633610...37511690680

.0.18.2114..108006..10872238...888633610...75341251814.6484756891722

.0.56.9226.1202184.222626294.37511690680.6484756891722

Links

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

Formula

Empirical for column k:

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

k=3: [order 19]

k=4: [order 95] for n>96

Example

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

Crossrefs

Sequence in context: A337113 A285244 A263148 * A317573 A032337 A380955

Adjacent sequences: A230816 A230817 A230818 * A230820 A230821 A230822

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 30 2013

Status

approved