A216031 T(n,k) is the number of horizontal, vertical and diagonal neighbor colorings of the odd squares of an n X k array with new integer colors introduced in row major order.

1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 5, 4, 5, 1, 2, 12, 29, 29, 12, 2, 2, 42, 97, 371, 97, 42, 2, 5, 136, 1534, 6150, 6150, 1534, 136, 5, 5, 602, 7050, 167130, 146327, 167130, 7050, 602, 5, 15, 2440, 188835, 5219070, 30312074, 30312074, 5219070, 188835, 2440, 15, 15, 12840

Offset: 1

Author

R. H. Hardin, Aug 30 2012

Keywords

• nonn
• tabl

Examples

			Table starts:
..1.....1........1...........1............1.............2.............2
..1.....2........2...........5...........12............42...........136
..1.....2........4..........29...........97..........1534..........7050
..1.....5.......29.........371.........6150........167130.......5219070
..1....12.......97........6150.......146327......30312074....1355988481
..2....42.....1534......167130.....30312074...10311562327.4761748786964
..2...136.....7050.....5219070...1355988481.4761748786964
..5...602...188835...233834847.609400419815
..5..2440..1084180.11412814314
.15.12840.42756208
.15.61912
.52
Some solutions for n=4 and k=4:
..x..0..x..1....x..0..x..1....x..0..x..1....x..0..x..1....x..0..x..1
..2..x..1..x....2..x..3..x....0..x..2..x....0..x..1..x....0..x..1..x
..x..1..x..2....x..1..x..4....x..3..x..0....x..2..x..0....x..1..x..0
..0..x..2..x....3..x..2..x....4..x..0..x....3..x..4..x....1..x..2..x
		

Links

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

Crossrefs

Column 1 is A000110(floor((n-2)/2)) for n>1.

Even squares: A215959.