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A216612 T(n,k)=Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of an nXk array with new integer colors introduced in row major order.

%I A216612 #6 Jul 22 2025 23:33:26
%S A216612 1,1,1,1,1,1,1,1,2,2,1,2,2,5,2,2,5,15,20,15,5,2,15,41,203,67,52,5,5,
%T A216612 52,716,3429,4140,1335,203,15,5,203,2847,83440,83437,115975,6097,877,
%U A216612 15,15,877,83440,2711768,18171918,20880505,4213597,192713,4140,52,15,4140
%N A216612 T(n,k)=Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of an nXk array with new integer colors introduced in row major order.
%C A216612 Table starts
%C A216612 ...1......1.........1............1..............1................2
%C A216612 ...1......1.........1............2..............5...............15
%C A216612 ...1......2.........2...........15.............41..............716
%C A216612 ...2......5........20..........203...........3429............83440
%C A216612 ...2.....15........67.........4140..........83437.........18171918
%C A216612 ...5.....52......1335.......115975.......20880505.......6423127757
%C A216612 ...5....203......6097......4213597......942420901....3376465219485
%C A216612 ..15....877....192713....190899322...484968748793.2486327138729353
%C A216612 ..15...4140...1094076..10480142147.33862631596393
%C A216612 ..52..21147..49055292.682076806159
%C A216612 ..52.115975.329588907
%C A216612 .203.678570
%H A216612 R. H. Hardin, <a href="/A216612/b216612.txt">Table of n, a(n) for n = 1..96</a>
%e A216612 Some solutions for n=4 k=4
%e A216612 ..x..0..x..1....x..0..x..1....x..0..x..1....x..0..x..1....x..0..x..1
%e A216612 ..2..x..3..x....2..x..3..x....1..x..2..x....2..x..3..x....1..x..2..x
%e A216612 ..x..4..x..2....x..1..x..2....x..0..x..3....x..4..x..0....x..3..x..4
%e A216612 ..5..x..6..x....4..x..3..x....2..x..1..x....2..x..5..x....0..x..2..x
%Y A216612 Column 2 is A000110(n-1)
%Y A216612 Column 4 is A020557(n-1)
%Y A216612 Column 6 is A208051
%Y A216612 Row 2 is A000110(n-2)
%Y A216612 Row 4 is A216462
%Y A216612 Row 6 is A216464
%Y A216612 Even squares: A216460
%K A216612 nonn,tabl
%O A216612 1,9
%A A216612 _R. H. Hardin_ Sep 10 2012