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%I #10 Mar 15 2018 04:47:22
%S 16,676,28564,1206964,50999956,2154990196,91058563924,3847656513844,
%T 162581749707796,6869850581244916,290283793189916884,
%U 12265868026121849524,518291141165452870036,21900260661415244606836
%N Number of n X 3 0..4 arrays with no entry increasing mod 5 by 4 rightwards or downwards, starting with upper left zero.
%C Column 3 of A222144.
%H R. H. Hardin, <a href="/A222139/b222139.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 45*a(n-1) - 116*a(n-2).
%F Conjectures from _Colin Barker_, Mar 14 2018: (Start)
%F G.f.: 4*x*(4 - 11*x) / (1 - 45*x + 116*x^2).
%F a(n) = (2^(-1-n)*((45-sqrt(1561))^n*(-433+11*sqrt(1561)) + (45+sqrt(1561))^n*(433+11*sqrt(1561)))) / (29*sqrt(1561)).
%F (End)
%e Some solutions for n=3:
%e 0 2 4 0 1 1 0 1 4 0 0 2 0 1 3 0 0 0 0 3 4
%e 1 2 0 2 4 1 1 4 0 2 2 2 3 1 1 3 3 1 2 3 4
%e 1 3 1 3 1 2 3 0 1 3 0 2 1 4 1 3 1 1 2 0 1
%Y Cf. A222144.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 09 2013