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A204973 Number of nX3 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..2 introduced in row major order.

%I A204973 #8 Jul 22 2025 18:28:48
%S A204973 4,96,1217,16813,226908,3074889,41618941,563504926,7628868673,
%T A204973 103284942785,1398329242622,18931424557397,256304779809413,
%U A204973 3470006246394670,46978999502038957,636029536681800861
%N A204973 Number of nX3 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..2 introduced in row major order.
%C A204973 Column 3 of A204978
%H A204973 R. H. Hardin, <a href="/A204973/b204973.txt">Table of n, a(n) for n = 1..210</a>
%F A204973 Empirical: a(n) = 9*a(n-1) +79*a(n-2) -165*a(n-3) -1117*a(n-4) +1506*a(n-5) +4665*a(n-6) -8530*a(n-7) +2842*a(n-8) +16415*a(n-9) -52874*a(n-10) -90975*a(n-11) +139014*a(n-12) -2762*a(n-13) -188806*a(n-14) +657130*a(n-15) -216610*a(n-16) -282088*a(n-17) +299084*a(n-18) -320888*a(n-19) -25488*a(n-20) +130096*a(n-21) -166448*a(n-22) -3680*a(n-23) +14752*a(n-24) -23360*a(n-25) +12288*a(n-26) +6144*a(n-27)
%e A204973 Some solutions for n=5
%e A204973 ..0..1..2....0..0..1....0..1..0....0..0..1....0..1..1....0..0..1....0..0..1
%e A204973 ..0..2..1....0..1..1....2..1..2....2..0..0....0..1..2....0..0..1....1..2..2
%e A204973 ..1..2..0....2..2..0....2..2..1....2..1..2....2..2..0....1..1..2....2..1..2
%e A204973 ..1..0..0....0..1..2....0..1..1....1..1..2....0..1..1....2..1..1....2..2..0
%e A204973 ..2..2..1....0..1..1....0..0..2....1..2..0....0..2..1....0..0..2....0..1..1
%K A204973 nonn
%O A204973 1,1
%A A204973 _R. H. Hardin_ Jan 21 2012