A203878 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..3 introduced in row major order

7, 55, 55, 487, 1135, 487, 4375, 23815, 23815, 4375, 39367, 500095, 1166887, 500095, 39367, 354295, 10501975, 57177415, 57177415, 10501975, 354295, 3188647, 220541455, 2801693287, 6542729803, 2801693287, 220541455, 3188647, 28697815

Offset

1,1

Comments

Table starts

........7..........55.............487................4375

.......55........1135...........23815..............500095

......487.......23815.........1166887............57177415

.....4375......500095........57177415..........6542729803

....39367....10501975......2801693287........748675224487

...354295...220541455....137282971015......85671438703075

..3188647..4631370535...6726865579687....9803443695486967

.28697815.97258781215.329616413404615.1121815509393271267

Links

R. H. Hardin, Table of n, a(n) for n = 1..127

Formula

Empirical for column k:

k=1: a(n) = 6*9^(n-1) +1

k=2: a(n) = 54*21^(n-1) +1

k=3: a(n) = 486*49^(n-1) +1

k=4: a(n) = 118*a(n-1) -117*a(n-2) -34398*a(n-3) +120834*a(n-4) -86436*a(n-5)

k=5: a(n) = 304*a(n-1) -8430*a(n-2) -386764*a(n-3) +4486195*a(n-4) +17085516*a(n-5) -113413636*a(n-6) +92236816*a(n-7)

k=6: (order 17 recurrence)

Example

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

Crossrefs

Column 1 is A199564(n-1)

Sequence in context: A182124 A303889 A198149 * A043077 A192718 A014637

Adjacent sequences: A203875 A203876 A203877 * A203879 A203880 A203881

Keyword

nonn,tabl

Author

R. H. Hardin Jan 07 2012

Status

approved