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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
12
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Feb 14 2012
STATUS
approved