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T(n,k)=Number of diagonal and antidiagonal neighbor colorings of the odd squares of an nXk array with new integer colors introduced in row major order
6

%I #4 Aug 27 2012 10:59:47

%S 1,1,1,1,1,1,2,2,2,2,2,5,4,5,2,5,15,42,42,15,5,5,52,136,602,136,52,5,

%T 15,203,2906,12840,12840,2906,203,15,15,877,12840,373780,322768,

%U 373780,12840,877,15,52,4140,433252,14050312,87852626,87852626,14050312,433252

%N T(n,k)=Number of diagonal and antidiagonal neighbor colorings of the odd squares of an nXk array with new integer colors introduced in row major order

%C Table starts

%C ..1.....1.........1.............2..................2.......................5

%C ..1.....1.........2.............5.................15......................52

%C ..1.....2.........4............42................136....................2906

%C ..2.....5........42...........602..............12840..................373780

%C ..2....15.......136.........12840.............322768................87852626

%C ..5....52......2906........373780...........87852626.............33093356640

%C ..5...203.....12840......14050312.........4044766240..........18383354944364

%C .15...877....433252.....656404264......2227156082842.......14216420563705724

%C .15..4140...2387180...37060650272....157752739276184....14670987605491079080

%C .52.21147.113503692.2475181138384.148049849095504726.19558496206477343793824

%H R. H. Hardin, <a href="/A215924/b215924.txt">Table of n, a(n) for n = 1..127</a>

%e Some solutions for n=3 k=4

%e ..x..0..x..1....x..0..x..0....x..0..x..1....x..0..x..1....x..0..x..1

%e ..1..x..2..x....1..x..2..x....2..x..3..x....2..x..3..x....2..x..2..x

%e ..x..3..x..1....x..3..x..0....x..0..x..1....x..4..x..0....x..1..x..1

%Y Column 2 is A000110(n-1)

%Y Column 4 is A208302

%Y Column 6 is A215902

%Y Even squares: A215904

%K nonn,tabl

%O 1,7

%A _R. H. Hardin_ Aug 27 2012