A209650 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically.

2, 4, 4, 6, 16, 6, 9, 36, 36, 8, 14, 81, 102, 64, 10, 22, 196, 270, 216, 100, 12, 35, 484, 798, 630, 390, 144, 14, 56, 1225, 2354, 2156, 1215, 636, 196, 16, 90, 3136, 7210, 7128, 4690, 2079, 966, 256, 18, 145, 8100, 22232, 24990, 16830, 8904, 3276, 1392, 324, 20, 234

Offset: 1

Author

R. H. Hardin Mar 11 2012

Keywords

• nonn
• tabl

Comments

Table starts

..2...4....6....9....14.....22.....35......56.......90......145.......234

..4..16...36...81...196....484...1225....3136.....8100....21025.....54756

..6..36..102..270...798...2354...7210...22232....69570...218950....693810

..8..64..216..630..2156...7128..24990...87136...311040..1112150...4018716

.10.100..390.1215..4690..16830..65765..251160...994050..3911375..15639390

.12.144..636.2079..8904..34012.145775..597856..2579940.10954895..47622744

.14.196..966.3276.15386..61754.287140.1247736..5805450.26247900.122620446

.16.256.1392.4860.24808.103664.518700.2364992.11769120.56106300.279344520

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..2828

Crossrefs

Column 2 is A016742

Column 3 is A086113

Row 1 is A001611(n+2)

Row 2 is A207436

Row 3 is A207747

Formula

Empirical for column k:

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

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

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

k=4: a(n) = 9*n^3 + (9/2)*n^2 - (9/2)*n

k=5: a(n) = (7/2)*n^4 + 21*n^3 - (7/2)*n^2 - 7*n

k=6: a(n) = 22*n^4 + (88/3)*n^3 - 22*n^2 - (22/3)*n

k=7: a(n) = 7*n^5 + 70*n^4 + (35/3)*n^3 - (105/2)*n^2 - (7/6)*n