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A208429 Number of nX3 0..2 arrays with new values 0..2 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).

%I A208429 #7 Jun 02 2025 07:44:31
%S A208429 5,54,129,339,1123,4155,15273,55715,205199,758647,2804053,10360467,
%T A208429 38311103,141717367,524247989,1939302323,7174276855,26541315667,
%U A208429 98190495765,363259275051,1343896481903,4971825005443,18393576694105
%N A208429 Number of nX3 0..2 arrays with new values 0..2 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).
%C A208429 Column 3 of A208434
%H A208429 R. H. Hardin, <a href="/A208429/b208429.txt">Table of n, a(n) for n = 1..210</a>
%F A208429 Empirical: a(n) = 3*a(n-1) +8*a(n-2) -18*a(n-3) -17*a(n-5) -116*a(n-6) +256*a(n-7) +184*a(n-8) -335*a(n-9) +260*a(n-10) -644*a(n-11) -368*a(n-12) +2013*a(n-13) -564*a(n-14) -1664*a(n-15) -1063*a(n-16) +1284*a(n-17) +3156*a(n-18) -1962*a(n-19) -256*a(n-20) +1020*a(n-21) -1448*a(n-22) -96*a(n-23) +144*a(n-24) +352*a(n-25) -128*a(n-26) for n>28
%e A208429 Some solutions for n=4
%e A208429 ..0..1..0....0..1..2....0..0..0....0..0..0....0..0..0....0..0..1....0..0..0
%e A208429 ..2..1..2....1..2..1....1..1..1....1..2..1....1..1..2....0..0..2....1..0..2
%e A208429 ..0..1..0....0..1..0....2..1..2....2..2..2....1..2..2....1..2..2....1..1..2
%e A208429 ..2..1..2....1..0..1....0..2..0....0..0..0....0..0..2....1..1..2....1..0..2
%K A208429 nonn
%O A208429 1,1
%A A208429 _R. H. Hardin_ Feb 26 2012