A230805 T(n,k)=Number of nXk 0..3 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, and upper left element zero

0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 16, 14, 16, 0, 0, 34, 40, 40, 34, 0, 0, 154, 298, 1370, 298, 154, 0, 0, 432, 1546, 10448, 10448, 1546, 432, 0, 0, 1618, 8704, 183088, 243746, 183088, 8704, 1618, 0, 0, 5058, 50450, 2045378, 6832578, 6832578, 2045378, 50450, 5058, 0, 0

Offset

1,5

Comments

Table starts

.0....0.....0........0..........0.............0.............0.............0

.0....2.....2.......16.........34...........154...........432..........1618

.0....2....14.......40........298..........1546..........8704.........50450

.0...16....40.....1370......10448........183088.......2045378......29175688

.0...34...298....10448.....243746.......6832578.....180981600....4943014834

.0..154..1546...183088....6832578.....485186602...25669880656.1576356652138

.0..432..8704..2045378..180981600...25669880656.3006220926554

.0.1618.50450.29175688.4943014834.1576356652138

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

k=2: a(n) = 2*a(n-1) +6*a(n-2) -5*a(n-3)

k=3: [order 13]

k=4: [order 68]

Example

Some solutions for n=4 k=4
..0..1..3..0....0..1..1..2....0..3..2..1....0..1..3..0....0..3..2..3
..3..2..2..1....3..2..0..3....1..2..3..0....3..2..2..1....1..2..1..0
..1..0..1..2....3..2..0..3....3..0..0..1....0..1..2..3....0..3..0..3
..2..3..0..3....0..1..1..2....2..1..3..2....3..2..1..0....3..2..1..2

Crossrefs

Sequence in context: A216800 A230831 A230899 * A230994 A337509 A144734

Adjacent sequences: A230802 A230803 A230804 * A230806 A230807 A230808

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 30 2013

Status

approved