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A208353 T(n,k) is the number of n X k 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).

%I A208353 #11 Oct 15 2024 15:42:10
%S A208353 1,2,2,5,15,5,15,100,100,15,51,868,1095,868,51,187,7780,12625,12625,
%T A208353 7780,187,715,69988,153237,230387,153237,69988,715,2795,629860,
%U A208353 1901508,4773885,4773885,1901508,629860,2795,11051,5668708,23658861,103672036
%N A208353 T(n,k) is the number of n X k 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).
%H A208353 R. H. Hardin, <a href="/A208353/b208353.txt">Table of n, a(n) for n = 1..83</a>
%e A208353 Table starts:
%e A208353 ....1.......2.........5..........15.............51............187
%e A208353 ....2......15.......100.........868...........7780..........69988
%e A208353 ....5.....100......1095.......12625.........153237........1901508
%e A208353 ...15.....868.....12625......230387........4773885......103672036
%e A208353 ...51....7780....153237.....4773885......191586797.....8045978096
%e A208353 ..187...69988...1901508...103672036.....8045978096...647640659639
%e A208353 ..715..629860..23658861..2280287753...340596199800.52428246114853
%e A208353 .2795.5668708.294608660.50481169071.14513602070899
%e A208353 Some solutions for n=4 and k=3:
%e A208353 ..0..0..0....0..0..0....0..0..0....0..0..0....0..1..0....0..0..0....0..0..0
%e A208353 ..1..0..1....1..1..1....1..2..1....1..1..1....1..2..2....1..1..1....1..0..1
%e A208353 ..2..1..2....2..1..2....2..1..3....2..1..2....3..2..2....2..1..2....2..2..2
%e A208353 ..1..2..1....3..2..3....0..0..1....0..2..0....1..3..0....3..2..0....1..2..3
%Y A208353 Main diagonal is A208346.
%Y A208353 Columns 1..7 are A007581(n-1), A208347, A208348, A208349, A208350, A208351, A208352.
%K A208353 nonn,tabl
%O A208353 1,2
%A A208353 _R. H. Hardin_, Feb 25 2012