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%I #5 Mar 31 2012 12:36:58
%S 7,55,55,487,1135,487,4375,23815,23815,4375,39367,500095,1166887,
%T 500095,39367,354295,10501975,57177415,57177415,10501975,354295,
%U 3188647,220541455,2801693287,6542729803,2801693287,220541455,3188647,28697815
%N 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
%C Table starts
%C ........7..........55.............487................4375
%C .......55........1135...........23815..............500095
%C ......487.......23815.........1166887............57177415
%C .....4375......500095........57177415..........6542729803
%C ....39367....10501975......2801693287........748675224487
%C ...354295...220541455....137282971015......85671438703075
%C ..3188647..4631370535...6726865579687....9803443695486967
%C .28697815.97258781215.329616413404615.1121815509393271267
%H R. H. Hardin, <a href="/A203878/b203878.txt">Table of n, a(n) for n = 1..127</a>
%F Empirical for column k:
%F k=1: a(n) = 6*9^(n-1) +1
%F k=2: a(n) = 54*21^(n-1) +1
%F k=3: a(n) = 486*49^(n-1) +1
%F k=4: a(n) = 118*a(n-1) -117*a(n-2) -34398*a(n-3) +120834*a(n-4) -86436*a(n-5)
%F 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)
%F k=6: (order 17 recurrence)
%e Some solutions for n=4 k=3
%e ..0..1..2..1....0..1..0..0....0..0..1..0....0..0..0..0....0..1..1..0
%e ..2..1..2..0....2..2..3..2....2..2..1..0....1..1..2..1....0..2..2..2
%e ..3..3..2..1....1..1..0..0....3..3..1..0....2..0..2..0....3..3..1..1
%e ..0..0..0..1....3..2..2..3....0..0..1..2....3..3..2..1....0..0..2..3
%e ..3..1..2..1....3..1..1..3....1..3..1..2....2..1..2..3....3..1..1..3
%Y Column 1 is A199564(n-1)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Jan 07 2012
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