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T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any antidiagonal neighbor (colorings ignoring permutations of colors)
8

%I #5 Mar 31 2012 12:37:24

%S 1,2,2,5,10,5,15,114,114,15,52,2066,9089,2066,52,203,52922,1515903,

%T 1515903,52922,203,877,1788850,435411946,3038188519,435411946,1788850,

%U 877,4140,76282138,193010377345,12766857248692,12766857248692

%N T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any antidiagonal neighbor (colorings ignoring permutations of colors)

%C Table starts

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

%C ....2.........10................114.......................2066

%C ....5........114...............9089....................1515903

%C ...15.......2066............1515903.................3038188519

%C ...52......52922..........435411946.............12766857248692

%C ..203....1788850.......193010377345..........96847533172181917

%C ..877...76282138....122941305336223.....1203020866861467699281

%C .4140.3974779402.106980807941644808.22838542212752073231771562

%H R. H. Hardin, <a href="/A208788/b208788.txt">Table of n, a(n) for n = 1..84</a>

%e Some solutions for n=4 k=3

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

%e ..1..1..0....1..1..0....1..2..0....1..1..0....1..1..0....1..1..0....1..0..0

%e ..2..1..0....2..1..0....0..1..0....0..1..0....2..1..0....0..1..0....1..2..0

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

%Y Column 1 is A000110

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ Mar 01 2012