A277767 T(n,k)=Number of nXk 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

0, 0, 0, 0, 1, 0, 0, 4, 2, 0, 0, 18, 17, 14, 0, 0, 80, 204, 330, 56, 0, 0, 356, 1989, 9741, 3666, 284, 0, 0, 1584, 21141, 275018, 270291, 46289, 1304, 0, 0, 7048, 220549, 7824415, 20049229, 8971150, 560809, 6248, 0, 0, 31360, 2292380, 221983169, 1487830718

Offset

1,8

Comments

Table starts

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

.0......1..........4............18................80.................356

.0......2.........17...........204..............1989...............21141

.0.....14........330..........9741............275018.............7824415

.0.....56.......3666........270291..........20049229..........1487830718

.0....284......46289.......8971150........1762881313........343944986355

.0...1304.....560809.....280603511......145416104585......74591651561541

.0...6248....6883464....8946059000....12253138042478...16513537201433122

.0..29408...84161576..283436060320..1025207978301185.3631417278822015869

.0.139472.1030163755.8998418743638.85977721285058269

Links

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

Formula

Empirical for column k:

k=2: a(n) = 4*a(n-1) +6*a(n-2) -12*a(n-3)

k=3: [order 11]

k=4: [order 44] for n>45

Empirical for row n:

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

n=3: [order 18]

n=4: [order 98]

Example

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

Crossrefs

Row 2 is A090017(n-1).

Sequence in context: A256269 A256279 A363436 * A107088 A137986 A330768

Adjacent sequences: A277764 A277765 A277766 * A277768 A277769 A277770

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 29 2016

Status

approved