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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 2 is A016742

Column 3 is A086113

Row 1 is A038718(n+2)

Sequence in context: A207305 A207391 A207938 * A209650 A207599 A207703

Adjacent sequences: A207065 A207066 A207067 * A207069 A207070 A207071

Keyword

nonn,tabl

Author

R. H. Hardin Feb 14 2012

Status

approved