A207599 T(n,k) = Number of n X k 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.

2, 4, 4, 6, 16, 6, 9, 36, 36, 8, 15, 81, 90, 64, 10, 25, 225, 225, 168, 100, 12, 40, 625, 825, 441, 270, 144, 14, 64, 1600, 3025, 1995, 729, 396, 196, 16, 104, 4096, 9240, 9025, 3915, 1089, 546, 256, 18, 169, 10816, 28224, 30400, 21025, 6765, 1521, 720, 324, 20, 273

Offset

1,1

Comments

Table starts

..2...4...6....9....15.....25.....40......64......104......169.......273

..4..16..36...81...225....625...1600....4096....10816....28561.....74529

..6..36..90..225...825...3025...9240...28224....93912...312481....997815

..8..64.168..441..1995...9025..30400..102400...403520..1590121...5746377

.10.100.270..729..3915..21025..75400..270400..1223560..5536609..21791133

.12.144.396.1089..6765..42025.157440..589824..3005184.15311569..64177113

.14.196.546.1521.10725..75625.292600.1132096..6404216.36228361.159389139

.16.256.720.2025.15975.126025.499840.1982464.12318592.76545001.350003745

Links

R. H. Hardin, Table of n, a(n) for n = 1..1250

Formula

Empirical for column k:

k=1: a(n) = 2*n

k=2: a(n) = 4*n^2

k=3: a(n) = 12*n^2 - 6*n

k=4: a(n) = 36*n^2 - 36*n + 9

k=5: a(n) = 30*n^3 + 15*n^2 - 45*n + 15

k=6: a(n) = 25*n^4 + 50*n^3 - 25*n^2 - 50*n + 25

k=7: a(n) = 120*n^4 + 40*n^3 - 200*n^2 + 80*n

Example

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

Crossrefs

Column 2 is A016742.

Column 3 is A152746.

Column 4 is A016946(n-1).

Row 1 is A006498(n+2).

Row 2 is A189145(n+2).

Sequence in context: A207938 A207068 A209650 * A207703 A267719 A207752

Adjacent sequences: A207596 A207597 A207598 * A207600 A207601 A207602

Keyword

nonn,tabl

Author

R. H. Hardin Feb 19 2012

Status

approved