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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.
8
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 07 2012
STATUS
approved