A209727 T(n,k) = 1/4 the number of (n+1) X (k+1) 0..2 arrays with every 2 X 2 subblock having distinct clockwise edge differences.

2, 3, 3, 4, 4, 4, 6, 5, 5, 6, 8, 7, 6, 7, 8, 12, 9, 8, 8, 9, 12, 16, 13, 10, 10, 10, 13, 16, 24, 17, 14, 12, 12, 14, 17, 24, 32, 25, 18, 16, 14, 16, 18, 25, 32, 48, 33, 26, 20, 18, 18, 20, 26, 33, 48, 64, 49, 34, 28, 22, 22, 22, 28, 34, 49, 64, 96, 65, 50, 36, 30, 26, 26, 30, 36, 50, 65, 96

Offset: 1

Author

R. H. Hardin, Mar 12 2012

Keywords

• nonn
• tabl

Comments

Table starts

..2..3..4..6..8.12.16.24.32.48.64..96.128.192.256.384.512.768.1024.1536.2048

..3..4..5..7..9.13.17.25.33.49.65..97.129.193.257.385.513.769.1025.1537.2049

..4..5..6..8.10.14.18.26.34.50.66..98.130.194.258.386.514.770.1026.1538.2050

..6..7..8.10.12.16.20.28.36.52.68.100.132.196.260.388.516.772.1028.1540.2052

..8..9.10.12.14.18.22.30.38.54.70.102.134.198.262.390.518.774.1030.1542.2054

.12.13.14.16.18.22.26.34.42.58.74.106.138.202.266.394.522.778.1034.1546.2058

.16.17.18.20.22.26.30.38.46.62.78.110.142.206.270.398.526.782.1038.1550.2062

.24.25.26.28.30.34.38.46.54.70.86.118.150.214.278.406.534.790.1046.1558.2070

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1512

Crossrefs

Column 1 is A029744(n+1).

Diagonal is A027383.

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-2).

k=2..7: a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3).