A207024 T(n,k) = Number of n X k 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

2, 4, 4, 6, 16, 6, 9, 36, 36, 8, 13, 81, 90, 64, 10, 18, 169, 252, 168, 100, 12, 25, 324, 624, 558, 270, 144, 14, 34, 625, 1350, 1586, 1035, 396, 196, 16, 46, 1156, 3025, 3726, 3315, 1719, 546, 256, 18, 62, 2116, 6256, 9450, 8280, 6123, 2646, 720, 324, 20, 83, 3844

Offset: 1

Author

R. H. Hardin, Feb 14 2012

Keywords

• nonn
• tabl

Comments

Table starts

..2...4...6....9....13....18.....25.....34......46......62.......83......111

..4..16..36...81...169...324....625...1156....2116....3844.....6889....12321

..6..36..90..252...624..1350...3025...6256...12788...25792....50630....99012

..8..64.168..558..1586..3726...9450..21318...47518..104470...220531...464202

.10.100.270.1035..3315..8280..23400..56814..136114..322834...725005..1627260

.12.144.396.1719..6123.16038..49925.129302..329498..836938..1984447..4716834

.14.196.546.2646.10374.28224..95900.263228..707756.1914436..4765030.11929281

.16.256.720.3852.16484.46260.170300.492932.1389476.3984244.10362550.27202659

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1984

Crossrefs

Column 2 is A016742.

Column 3 is A152746.

Row 1 is A171861(n+1).

Formula

Empirical for column k:

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

k=2: a(n) = 4*n^2

k=3: a(n) = 12*n^2 - 6*n

k=4: a(n) = 6*n^3 + (27/2)*n^2 - (21/2)*n

k=5: a(n) = (13/6)*n^4 + 13*n^3 + (52/3)*n^2 - (39/2)*n

k=6: a(n) = (33/4)*n^4 + (45/2)*n^3 + (75/4)*n^2 - (63/2)*n

k=7: a(n) = (55/24)*n^5 + (75/4)*n^4 + (275/8)*n^3 + (75/4)*n^2 - (295/6)*n