A216031 T(n,k)=Number of horizontal, vertical and diagonal neighbor colorings of the odd squares of an nXk 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

1,5

Comments

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

Links

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

Example

Some solutions for n=4 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

Crossrefs

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

Even squares: A215959

Sequence in context: A156074 A051287 A278218 * A263985 A176261 A264837

Adjacent sequences: A216028 A216029 A216030 * A216032 A216033 A216034

Keyword

nonn,tabl

Author

R. H. Hardin Aug 30 2012

Status

approved