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A215959 T(n,k)=Number of horizontal, vertical and diagonal neighbor colorings of the even squares of an nXk array with new integer colors introduced in row major order.

%I A215959 #8 Jul 22 2025 23:28:44
%S A215959 1,1,1,1,1,1,1,2,2,1,2,4,10,4,2,2,12,29,29,12,2,5,34,366,313,366,34,5,
%T A215959 5,136,1534,6150,6150,1534,136,5,15,500,35167,145563,847594,145563,
%U A215959 35167,500,15,15,2440,188835,5219070,30312074,30312074,5219070,188835,2440,15
%N A215959 T(n,k)=Number of horizontal, vertical and diagonal neighbor colorings of the even squares of an nXk array with new integer colors introduced in row major order.
%C A215959 Table starts
%C A215959 ..1.....1........1...........1............2.............2.............5
%C A215959 ..1.....1........2...........4...........12............34...........136
%C A215959 ..1.....2.......10..........29..........366..........1534.........35167
%C A215959 ..1.....4.......29.........313.........6150........145563.......5219070
%C A215959 ..2....12......366........6150.......847594......30312074...10289785215
%C A215959 ..2....34.....1534......145563.....30312074....9260821180.4761748786964
%C A215959 ..5...136....35167.....5219070..10289785215.4761748786964
%C A215959 ..5...500...188835...208181894.609400419815
%C A215959 .15..2440..6618472.11412814314
%C A215959 .15.10900.42756208
%H A215959 R. H. Hardin, <a href="/A215959/b215959.txt">Table of n, a(n) for n = 1..84</a>
%e A215959 Some solutions for n=4 k=4
%e A215959 ..0..x..1..x....0..x..1..x....0..x..1..x....0..x..1..x....0..x..1..x
%e A215959 ..x..2..x..3....x..2..x..3....x..1..x..0....x..2..x..3....x..2..x..3
%e A215959 ..1..x..4..x....4..x..3..x....2..x..0..x....4..x..5..x....4..x..5..x
%e A215959 ..x..0..x..5....x..5..x..2....x..3..x..1....x..5..x..2....x..0..x..4
%Y A215959 Column 1 is A000110(floor((n-1)/2))
%Y A215959 Odd squares: A216031
%K A215959 nonn,tabl
%O A215959 1,8
%A A215959 _R. H. Hardin_ Aug 28 2012