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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 2 is A016742

Column 3 is A086113

Row 1 is A006355(n+2)

Row 2 is A206981

Row 3 is A060521

Sequence in context: A207858 A208379 A207453 * A208501 A207589 A208069

Adjacent sequences: A208284 A208285 A208286 * A208288 A208289 A208290

Keyword

nonn,tabl

Author

R. H. Hardin Feb 25 2012

Status

approved