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A203835
T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements
8
45, 225, 225, 1125, 1971, 1125, 5625, 17289, 17289, 5625, 28125, 151659, 270333, 151659, 28125, 140625, 1330353, 4238721, 4238721, 1330353, 140625, 703125, 11669859, 66490965, 119606211, 66490965, 11669859, 703125, 3515625, 102368025
OFFSET
1,1
COMMENTS
Table starts
......45.......225.........1125...........5625.............28125
.....225......1971........17289.........151659...........1330353
....1125.....17289.......270333........4238721..........66490965
....5625....151659......4238721......119606211........3383285769
...28125...1330353.....66490965.....3383285769......173185290765
..140625..11669859...1043088057....95763046491.....8882824128417
..703125.102368025..16363800045..2710984443345...455911325162757
.3515625.897972507.256713156657.76749227497395.23404859123410809
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 9*5^n
k=2: a(n) = 9*a(n-1) -2*a(n-2)
k=3: a(n) = 19*a(n-1) -54*a(n-2) +32*a(n-3)
k=4: a(n) = 31*a(n-1) -24*a(n-2) -1612*a(n-3) +3816*a(n-4) +1152*a(n-5) -2784*a(n-6) +256*a(n-7)
k=5: (order 12 recurrence)
k=6: (order 28 recurrence)
k=7: (order 54 recurrence)
EXAMPLE
Some solutions for n=4 k=3
..0..2..0..1....2..1..0..0....0..1..2..0....0..0..2..0....2..1..0..2
..2..0..1..0....1..1..1..0....1..2..2..2....0..2..2..2....2..2..1..0
..0..2..0..1....2..1..2..1....0..1..2..2....1..0..2..2....1..2..2..1
..2..0..0..0....2..2..2..2....0..0..1..2....2..1..0..2....0..1..2..2
..2..2..0..1....1..2..1..2....2..0..0..1....1..2..1..0....2..0..1..2
CROSSREFS
Column 1 is A189274(n+2)
Sequence in context: A091197 A184539 A146302 * A087442 A334035 A280059
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Jan 06 2012
STATUS
approved