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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
10

%I #4 Sep 10 2012 11:31:46

%S 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 52,716,3429,4140,1335,203,15,5,203,2847,83440,83437,115975,6097,877,

%U 15,15,877,83440,2711768,18171918,20880505,4213597,192713,4140,52,15,4140

%N 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 Table starts

%C ...1......1.........1............1..............1................2

%C ...1......1.........1............2..............5...............15

%C ...1......2.........2...........15.............41..............716

%C ...2......5........20..........203...........3429............83440

%C ...2.....15........67.........4140..........83437.........18171918

%C ...5.....52......1335.......115975.......20880505.......6423127757

%C ...5....203......6097......4213597......942420901....3376465219485

%C ..15....877....192713....190899322...484968748793.2486327138729353

%C ..15...4140...1094076..10480142147.33862631596393

%C ..52..21147..49055292.682076806159

%C ..52.115975.329588907

%C .203.678570

%H R. H. Hardin, <a href="/A216612/b216612.txt">Table of n, a(n) for n = 1..96</a>

%e Some solutions for n=4 k=4

%e ..x..0..x..1....x..0..x..1....x..0..x..1....x..0..x..1....x..0..x..1

%e ..2..x..3..x....2..x..3..x....1..x..2..x....2..x..3..x....1..x..2..x

%e ..x..4..x..2....x..1..x..2....x..0..x..3....x..4..x..0....x..3..x..4

%e ..5..x..6..x....4..x..3..x....2..x..1..x....2..x..5..x....0..x..2..x

%Y Column 2 is A000110(n-1)

%Y Column 4 is A020557(n-1)

%Y Column 6 is A208051

%Y Row 2 is A000110(n-2)

%Y Row 4 is A216462

%Y Row 6 is A216464

%Y Even squares: A216460

%K nonn,tabl

%O 1,9

%A _R. H. Hardin_ Sep 10 2012