cp's OEIS Frontend

A216031 T(n,k) is the number of horizontal, vertical and diagonal neighbor colorings of the odd squares of an n X k array with new integer colors introduced in row major order.

%I A216031 #10 Oct 30 2024 08:06:41
%S A216031 1,1,1,1,2,1,1,2,2,1,1,5,4,5,1,2,12,29,29,12,2,2,42,97,371,97,42,2,5,
%T A216031 136,1534,6150,6150,1534,136,5,5,602,7050,167130,146327,167130,7050,
%U A216031 602,5,15,2440,188835,5219070,30312074,30312074,5219070,188835,2440,15,15,12840
%N A216031 T(n,k) is the number of horizontal, vertical and diagonal neighbor colorings of the odd squares of an n X k array with new integer colors introduced in row major order.
%H A216031 R. H. Hardin, <a href="/A216031/b216031.txt">Table of n, a(n) for n = 1..84</a>
%e A216031 Table starts:
%e A216031 ..1.....1........1...........1............1.............2.............2
%e A216031 ..1.....2........2...........5...........12............42...........136
%e A216031 ..1.....2........4..........29...........97..........1534..........7050
%e A216031 ..1.....5.......29.........371.........6150........167130.......5219070
%e A216031 ..1....12.......97........6150.......146327......30312074....1355988481
%e A216031 ..2....42.....1534......167130.....30312074...10311562327.4761748786964
%e A216031 ..2...136.....7050.....5219070...1355988481.4761748786964
%e A216031 ..5...602...188835...233834847.609400419815
%e A216031 ..5..2440..1084180.11412814314
%e A216031 .15.12840.42756208
%e A216031 .15.61912
%e A216031 .52
%e A216031 Some solutions for n=4 and k=4:
%e A216031 ..x..0..x..1....x..0..x..1....x..0..x..1....x..0..x..1....x..0..x..1
%e A216031 ..2..x..1..x....2..x..3..x....0..x..2..x....0..x..1..x....0..x..1..x
%e A216031 ..x..1..x..2....x..1..x..4....x..3..x..0....x..2..x..0....x..1..x..0
%e A216031 ..0..x..2..x....3..x..2..x....4..x..0..x....3..x..4..x....1..x..2..x
%Y A216031 Column 1 is A000110(floor((n-2)/2)) for n>1.
%Y A216031 Even squares: A215959.
%K A216031 nonn,tabl
%O A216031 1,5
%A A216031 _R. H. Hardin_, Aug 30 2012