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

Author

R. H. Hardin, Apr 16 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A005578(n-2)

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