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A215904 T(n,k)=Number of diagonal and antidiagonal neighbor colorings of the even squares of an nXk array with new integer colors introduced in row major order.

%I A215904 #10 Jul 22 2025 23:27:28
%S A215904 1,1,1,2,1,2,2,2,2,2,5,5,15,5,5,5,15,42,42,15,5,15,52,726,602,726,52,
%T A215904 15,15,203,2906,12840,12840,2906,203,15,52,877,84550,373780,2387217,
%U A215904 373780,84550,877,52,52,4140,433252,14050312,87852626,87852626,14050312,433252
%N A215904 T(n,k)=Number of diagonal and antidiagonal neighbor colorings of the even squares of an nXk array with new integer colors introduced in row major order.
%C A215904 Table starts
%C A215904 ...1......1...........2...............2..................5....................5
%C A215904 ...1......1...........2...............5.................15...................52
%C A215904 ...2......2..........15..............42................726.................2906
%C A215904 ...2......5..........42.............602..............12840...............373780
%C A215904 ...5.....15.........726...........12840............2387217.............87852626
%C A215904 ...5.....52........2906..........373780...........87852626..........33093356640
%C A215904 ..15....203.......84550........14050312........37060769357.......18383354944364
%C A215904 ..15....877......433252.......656404264......2227156082842....14216420563705724
%C A215904 ..52...4140....18378580.....37060650272...1701536105684377.14670987605491079080
%C A215904 ..52..21147...113503692...2475181138384.148049849095504726
%C A215904 .203.115975..6485270720.192262536609952
%C A215904 .203.678570.46538017584
%H A215904 R. H. Hardin, <a href="/A215904/b215904.txt">Table of n, a(n) for n = 1..112</a>
%e A215904 Some solutions for n=3 k=4
%e A215904 ..0..x..1..x....0..x..1..x....0..x..0..x....0..x..0..x....0..x..1..x
%e A215904 ..x..2..x..2....x..2..x..2....x..1..x..2....x..1..x..2....x..2..x..2
%e A215904 ..1..x..0..x....3..x..3..x....3..x..3..x....2..x..3..x....0..x..1..x
%Y A215904 Column 2 is A000110(n-1)
%Y A215904 Column 4 is A208302
%Y A215904 Odd squares: A215924
%K A215904 nonn,tabl
%O A215904 1,4
%A A215904 _R. H. Hardin_ Aug 26 2012