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%I #9 Jun 12 2018 09:49:44
%S 74,550,4220,32500,248940,1910922,14668206,112560786,863863526,
%T 6629842280,50880821560,390488098388,2996825524800,22999305690670,
%U 176509524902826,1354632729727342,10396208030732474,79786307537199012
%N Number of (n+1) X 3 0..2 arrays with no 2 X 2 subblock having the same number of equal edges as its horizontal or vertical neighbors, and new values 0..2 introduced in row major order.
%C Column 2 of A205590.
%H R. H. Hardin, <a href="/A205584/b205584.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) +24*a(n-2) +82*a(n-3) +83*a(n-4) -107*a(n-5) +30*a(n-6) +250*a(n-7).
%F Empirical g.f.: 2*x*(37 + 164*x + 397*x^2 + 286*x^3 - 541*x^4 + 165*x^5 + 1125*x^6) / (1 - 3*x - 24*x^2 - 82*x^3 - 83*x^4 + 107*x^5 - 30*x^6 - 250*x^7). - _Colin Barker_, Jun 12 2018
%e Some solutions for n=4:
%e ..0..0..0....0..0..1....0..0..0....0..0..0....0..0..0....0..1..2....0..0..1
%e ..1..0..0....0..2..2....0..1..2....0..0..1....1..0..0....0..2..0....2..0..2
%e ..2..0..2....2..0..2....2..1..2....1..2..0....1..2..0....2..2..1....2..1..0
%e ..2..0..1....2..0..1....1..0..2....1..2..1....2..1..0....0..1..2....2..2..2
%e ..0..1..1....1..0..0....1..1..0....0..0..2....0..1..1....0..1..0....1..0..0
%Y Cf. A205590.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 29 2012
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