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

Author

R. H. Hardin, Oct 29 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Row 2 is A090017(n-1).

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]