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A215924 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.

%I A215924 #6 Jul 22 2025 23:28:09
%S A215924 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 A215924 15,203,2906,12840,12840,2906,203,15,15,877,12840,373780,322768,
%U A215924 373780,12840,877,15,52,4140,433252,14050312,87852626,87852626,14050312,433252
%N A215924 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 A215924 Table starts
%C A215924 ..1.....1.........1.............2..................2.......................5
%C A215924 ..1.....1.........2.............5.................15......................52
%C A215924 ..1.....2.........4............42................136....................2906
%C A215924 ..2.....5........42...........602..............12840..................373780
%C A215924 ..2....15.......136.........12840.............322768................87852626
%C A215924 ..5....52......2906........373780...........87852626.............33093356640
%C A215924 ..5...203.....12840......14050312.........4044766240..........18383354944364
%C A215924 .15...877....433252.....656404264......2227156082842.......14216420563705724
%C A215924 .15..4140...2387180...37060650272....157752739276184....14670987605491079080
%C A215924 .52.21147.113503692.2475181138384.148049849095504726.19558496206477343793824
%H A215924 R. H. Hardin, <a href="/A215924/b215924.txt">Table of n, a(n) for n = 1..127</a>
%e A215924 Some solutions for n=3 k=4
%e A215924 ..x..0..x..1....x..0..x..0....x..0..x..1....x..0..x..1....x..0..x..1
%e A215924 ..1..x..2..x....1..x..2..x....2..x..3..x....2..x..3..x....2..x..2..x
%e A215924 ..x..3..x..1....x..3..x..0....x..0..x..1....x..4..x..0....x..1..x..1
%Y A215924 Column 2 is A000110(n-1)
%Y A215924 Column 4 is A208302
%Y A215924 Column 6 is A215902
%Y A215924 Even squares: A215904
%K A215924 nonn,tabl
%O A215924 1,7
%A A215924 _R. H. Hardin_ Aug 27 2012