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%I A233218 #7 Oct 10 2018 10:01:13
%S A233218 3,23,376,7222,147019,3054973,63927526,1340889772,28147567369,
%T A233218 591021089923,12410898114676,260625046992322,5473099292927719,
%U A233218 114934898294104873,2413631556174561826,50686253523654314872
%N A233218 Number of 2 X n 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.
%H A233218 R. H. Hardin, <a href="/A233218/b233218.txt">Table of n, a(n) for n = 1..210</a>
%F A233218 Empirical: a(n) = 29*a(n-1) - 175*a(n-2) + 147*a(n-3) for n>4.
%F A233218 Conjectures from _Colin Barker_, Oct 10 2018: (Start)
%F A233218 G.f.: x*(3 - 64*x + 234*x^2 - 98*x^3) / ((1 - x)*(1 - 7*x)*(1 - 21*x)).
%F A233218 a(n) = (2205 + 486*7^n + 125*21^n) / 3528 for n>1.
%F A233218 (End)
%e A233218 Some solutions for n=4:
%e A233218 ..0..1..2..4....0..1..0..4....0..1..2..2....0..1..2..4....0..1..2..1
%e A233218 ..2..1..0..1....0..1..2..1....1..0..2..2....2..2..4..3....1..2..0..1
%Y A233218 Row 2 of A233217.
%K A233218 nonn
%O A233218 1,1
%A A233218 _R. H. Hardin_, Dec 06 2013

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