A207068 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 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, 21, 196, 288, 216, 100, 12, 31, 441, 896, 720, 390, 144, 14, 46, 961, 2499, 2688, 1485, 636, 196, 16, 68, 2116, 6634, 8799, 6398, 2709, 966, 256, 18, 100, 4624, 17848, 27063, 23856, 13132, 4536, 1392, 324, 20, 147

Offset: 1

Author

R. H. Hardin Feb 14 2012

Keywords

• nonn
• tabl

Comments

Table starts

..2...4....6....9....14.....21.....31......46.......68......100.......147

..4..16...36...81...196....441....961....2116.....4624....10000.....21609

..6..36..102..288...896...2499...6634...17848....47192...122200....315315

..8..64..216..720..2688...8799..27063...84502...257584...762900...2246895

.10.100..390.1485..6398..23856..82739..291364...997288..3297100..10818024

.12.144..636.2709.13132..54684.210118..818892..3093184.11234900..40417797

.14.196..966.4536.24304.111426.468348.1992996..8204200.32364700.126207438

.16.256.1392.7128.41664.208026.947298.4356936.19360144.82226100.344542569

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1404

Crossrefs

Column 2 is A016742

Column 3 is A086113

Row 1 is A038718(n+2)

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) = (3/4)*n^4 + (15/2)*n^3 + (15/4)*n^2 - 3*n

k=5: a(n) = (7/30)*n^5 + 7*n^4 + (21/2)*n^3 - (56/15)*n

k=6: a(n) = (7/120)*n^6 + (147/40)*n^5 + (49/3)*n^4 + (91/8)*n^3 - (707/120)*n^2 - (91/20)*n

k=7: a(n) = (31/2520)*n^7 + (62/45)*n^6 + (4867/360)*n^5 + (2015/72)*n^4 + (1271/180)*n^3 - (4991/360)*n^2 - (713/140)*n