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%I #6 Mar 31 2012 12:37:29
%S 5,9,9,17,25,17,33,65,65,33,65,193,257,193,65,129,513,1025,1025,513,
%T 129,257,1537,4097,6145,4097,1537,257,513,4097,16385,32769,32769,
%U 16385,4097,513,1025,12289,65537,196609,262145,196609,65537,12289,1025,2049,32769
%N T(n,k)=Half the number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having exactly two distinct clockwise edge differences
%C Table starts
%C ...5.....9.....17......33........65........129.........257...........513
%C ...9....25.....65.....193.......513.......1537........4097.........12289
%C ..17....65....257....1025......4097......16385.......65537........262145
%C ..33...193...1025....6145.....32769.....196609.....1048577.......6291457
%C ..65...513...4097...32769....262145....2097153....16777217.....134217729
%C .129..1537..16385..196609...2097153...25165825...268435457....3221225473
%C .257..4097..65537.1048577..16777217..268435457..4294967297...68719476737
%C .513.12289.262145.6291457.134217729.3221225473.68719476737.1649267441665
%H R. H. Hardin, <a href="/A209534/b209534.txt">Table of n, a(n) for n = 1..7808</a>
%F Empirical: for odd columns k T(n,k) = 2^((n+1)*(k+1)/2)+1
%F Empirical for even columns k:
%F k=2: a(n) = a(n-1) +8*a(n-2) -8*a(n-3)
%F k=4: a(n) = a(n-1) +32*a(n-2) -32*a(n-3)
%F k=6: a(n) = a(n-1) +128*a(n-2) -128*a(n-3)
%F Apparently for even k a(n) = a(n-1) +2^(k+1)*a(n-2) -2^(k+1)*a(n-3)
%e Some solutions for n=4 k=3
%e ..1..2..1..2....0..1..2..1....2..0..2..0....1..2..1..2....0..1..0..1
%e ..2..1..0..1....1..0..1..0....0..2..0..2....2..1..2..1....1..2..1..2
%e ..1..2..1..0....2..1..0..1....2..0..2..0....1..2..1..2....2..1..0..1
%e ..2..1..2..1....1..0..1..0....0..2..0..2....2..1..2..1....1..2..1..2
%e ..1..2..1..2....2..1..0..1....2..0..2..0....1..2..1..0....2..1..0..1
%Y Column 1 is A000051(n+1)
%Y Column 3 is A052539(n+1)
%Y Column 5 is A062395(n+1)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Mar 10 2012
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