A277788 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) (1,-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, 3, 0, 0, 12, 12, 0, 0, 84, 80, 84, 0, 0, 498, 1434, 1434, 498, 0, 0, 3090, 20663, 79092, 20663, 3090, 0, 0, 18930, 309612, 3182256, 3182256, 309612, 18930, 0, 0, 116382, 4604554, 137510661, 352957610, 137510661, 4604554, 116382, 0, 0, 714810

Offset

1,5

Comments

Table starts

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

.0......3.........12.............84...............498..................3090

.0.....12.........80...........1434.............20663................309612

.0.....84.......1434..........79092...........3182256.............137510661

.0....498......20663........3182256.........352957610...........42007318111

.0...3090.....309612......137510661.......42007318111........13899171401510

.0..18930....4604554.....5841628899.....4917756016412......4515609963711003

.0.116382...68632481...249237125709...578187054139243...1473737617518590407

.0.714810.1022176517.10621140577245.67894823921434433.480374435720722263006

Links

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

Formula

Empirical for column k:

k=2: a(n) = 5*a(n-1) +8*a(n-2) -6*a(n-3)

k=3: [order 23] for n>24

k=4: [order 48] for n>50

Example

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

Crossrefs

Sequence in context: A123474 A363033 A321711 * A208848 A277945 A169777

Adjacent sequences: A277785 A277786 A277787 * A277789 A277790 A277791

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 31 2016

Status

approved