A230787 T(n,k)=Number of nXk 0..3 arrays x(i,j) with each element horizontally, vertically, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, and upper left element zero

0, 0, 0, 0, 6, 0, 0, 86, 86, 0, 0, 820, 3332, 820, 0, 0, 8154, 117372, 117372, 8154, 0, 0, 82576, 4321988, 14875702, 4321988, 82576, 0, 0, 833986, 159055144, 1986882996, 1986882996, 159055144, 833986, 0, 0, 8417644, 5846988064, 265749521034

Offset

1,5

Comments

Table starts

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

.0......6.........86............820...............8154..................82576

.0.....86.......3332.........117372............4321988..............159055144

.0....820.....117372.......14875702.........1986882996...........265749521034

.0...8154....4321988.....1986882996.......974259190594........477873113683628

.0..82576..159055144...265749521034....477873113683628.....859151087187859602

.0.833986.5846988064.35493529463278.234034971045993736.1541982081513444808180

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Formula

Empirical for column k:

k=2: a(n) = 10*a(n-1) -3*a(n-2) +44*a(n-3) -40*a(n-4) +8*a(n-5) -192*a(n-6)

k=3: [order 20]

k=4: [order 67]

Example

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

Crossrefs

Sequence in context: A229510 A358891 A358515 * A360424 A101109 A353224

Adjacent sequences: A230784 A230785 A230786 * A230788 A230789 A230790

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 30 2013

Status

approved