A241138 T(n,k)=Number of nXk 0..2 arrays with no element equal to the same number of vertical neighbors as horizontal neighbors, with new values 0..2 introduced in row major order

0, 1, 1, 1, 2, 1, 2, 5, 5, 2, 3, 17, 24, 17, 3, 6, 56, 152, 152, 56, 6, 11, 195, 935, 1670, 935, 195, 11, 22, 691, 6150, 19619, 19619, 6150, 691, 22, 43, 2476, 40504, 238607, 434444, 238607, 40504, 2476, 43, 86, 8941, 269481, 2939027, 9958520, 9958520, 2939027

Offset

1,5

Comments

Table starts

..0.....1........1..........2.............3..............6..............11

..1.....2........5.........17............56............195.............691

..1.....5.......24........152...........935...........6150...........40504

..2....17......152.......1670.........19619.........238607.........2939027

..3....56......935......19619........434444........9958520.......230889822

..6...195.....6150.....238607.......9958520......428855442.....18742128588

.11...691....40504....2939027.....230889822....18742128588...1546330012544

.22..2476...269481...36470565....5392206371...825015103540.128518782423157

.43..8941..1797120..454209512..126282435834.36426835430201

.86.32393.12006500.5665536042.2961490680709

Links

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

Formula

Empirical for column k:

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

k=2: a(n) = 4*a(n-1) +2*a(n-2) -11*a(n-3) -6*a(n-4) +8*a(n-5) for n>6

k=3: [order 26] for n>27

Example

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

Crossrefs

Column 1 is A005578(n-2)

Sequence in context: A228815 A241555 A277741 * A241349 A330405 A111934

Adjacent sequences: A241135 A241136 A241137 * A241139 A241140 A241141

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 16 2014

Status

approved