A208287 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

2, 4, 4, 6, 16, 6, 10, 36, 36, 8, 16, 100, 102, 64, 10, 26, 256, 378, 216, 100, 12, 42, 676, 1260, 984, 390, 144, 14, 68, 1764, 4374, 3984, 2090, 636, 196, 16, 110, 4624, 14946, 16872, 9900, 3900, 966, 256, 18, 178, 12100, 51384, 70216, 49130, 21096, 6650, 1392

Offset: 1

Author

R. H. Hardin Feb 25 2012

Keywords

• nonn
• tabl

Comments

Table starts

..2...4....6....10....16.....26......42.......68.......110........178

..4..16...36...100...256....676....1764.....4624.....12100......31684

..6..36..102...378..1260...4374...14946....51384....176238.....605022

..8..64..216...984..3984..16872...70216...294192...1229400....5142728

.10.100..390..2090..9900..49130..239490..1175440...5754050...28195750

.12.144..636..3900.21096.119580..665892..3733080..20874900..116842500

.14.196..966..6650.40376.256774.1604862.10095932..63357434..397965218

.16.256.1392.10608.71360.502416.3478160.24229696.168399632.1171405168

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1106

Crossrefs

Column 2 is A016742

Column 3 is A086113

Row 1 is A006355(n+2)

Row 2 is A206981

Row 3 is A060521

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) = (4/3)*n^4 + 10*n^3 + (2/3)*n^2 - 2*n

k=5: a(n) = (5/6)*n^5 + 9*n^4 + (91/6)*n^3 - 9*n^2

k=6: a(n) = (8/15)*n^6 + (23/3)*n^5 + (82/3)*n^4 + (1/3)*n^3 - (178/15)*n^2 + 2*n

k=7: a(n) = (61/180)*n^7 + (121/20)*n^6 + (1157/36)*n^5 + (425/12)*n^4 - (2923/90)*n^3 - (22/15)*n^2 + 2*n