A215959 T(n,k)=Number of horizontal, vertical and diagonal neighbor colorings of the even squares of an nXk array with new integer colors introduced in row major order

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 4, 10, 4, 2, 2, 12, 29, 29, 12, 2, 5, 34, 366, 313, 366, 34, 5, 5, 136, 1534, 6150, 6150, 1534, 136, 5, 15, 500, 35167, 145563, 847594, 145563, 35167, 500, 15, 15, 2440, 188835, 5219070, 30312074, 30312074, 5219070, 188835, 2440, 15

Offset

1,8

Comments

Table starts

..1.....1........1...........1............2.............2.............5

..1.....1........2...........4...........12............34...........136

..1.....2.......10..........29..........366..........1534.........35167

..1.....4.......29.........313.........6150........145563.......5219070

..2....12......366........6150.......847594......30312074...10289785215

..2....34.....1534......145563.....30312074....9260821180.4761748786964

..5...136....35167.....5219070..10289785215.4761748786964

..5...500...188835...208181894.609400419815

.15..2440..6618472.11412814314

.15.10900.42756208

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Example

Some solutions for n=4 k=4
..0..x..1..x....0..x..1..x....0..x..1..x....0..x..1..x....0..x..1..x
..x..2..x..3....x..2..x..3....x..1..x..0....x..2..x..3....x..2..x..3
..1..x..4..x....4..x..3..x....2..x..0..x....4..x..5..x....4..x..5..x
..x..0..x..5....x..5..x..2....x..3..x..1....x..5..x..2....x..0..x..4

Crossrefs

Column 1 is A000110(floor((n-1)/2))

Odd squares: A216031

Sequence in context: A294783 A172021 A325182 * A209555 A059594 A183760

Adjacent sequences: A215956 A215957 A215958 * A215960 A215961 A215962

Keyword

nonn,tabl

Author

R. H. Hardin Aug 28 2012

Status

approved