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T(n,k)=Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of an nXk array with new integer colors introduced in row major order
12

%I #6 Sep 10 2012 11:31:30

%S 1,1,1,1,1,2,1,1,2,2,2,2,7,5,5,2,5,15,20,15,5,5,15,203,203,322,52,15,

%T 5,52,716,3429,4140,1335,203,15,15,203,17733,83440,580479,115975,

%U 36401,877,52,15,877,83440,2711768,18171918,20880505,4213597,192713,4140,52,52

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

%C Table starts

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

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

%C ...2......2..........7...........15.............203..............716

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

%C ...5.....15........322.........4140..........580479.........18171918

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

%C ..15....203......36401......4213597......8195008751....3376465219485

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

%C ..52...4140....7712455..10480142147.348950573407587

%C ..52..21147...49055292.682076806159

%C .203.115975.2659544320

%C .203.678570

%H R. H. Hardin, <a href="/A216460/b216460.txt">Table of n, a(n) for n = 1..96</a>

%e Some solutions for n=4 k=4

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

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

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

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

%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 Odd squares: A216612

%K nonn,tabl

%O 1,6

%A _R. H. Hardin_ Sep 07 2012