%I #6 Jul 05 2012 06:18:20
%S 4,257,28278,3221873,367793014,41989913081,4793901053846,
%T 547309896088193,62485254609615222,7133814088846153097,
%U 814453006155085388566,92984438755466611752209,10615843744610501570047094
%N Number of 0..4 colorings on an nX4 array circular in the 4 direction with new values 0..4 introduced in row major order
%C Column 3 of A214141
%H R. H. Hardin, <a href="/A214136/b214136.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 129*a(n-1) -1759*a(n-2) +7575*a(n-3) -9064*a(n-4) +3120*a(n-5).
%F Empirical: G.f. -x*(4-259*x+2161*x^2-4226*x^3+1880*x^4) / ( (x-1) *(780*x^2-121*x+1) *(4*x^2-7*x+1) ). - _R. J. Mathar_, Jul 05 2012
%e Some solutions for n=4
%e ..0..1..0..1....0..1..2..3....0..1..0..1....0..1..0..1....0..1..0..2
%e ..2..3..4..3....4..2..4..2....2..0..3..0....1..2..1..2....3..4..1..4
%e ..1..2..3..4....3..1..0..1....4..3..1..2....0..1..3..4....0..3..4..2
%e ..2..3..2..0....1..2..1..0....0..4..0..4....3..4..1..0....4..0..1..3
%K nonn
%O 1,1
%A _R. H. Hardin_ Jul 05 2012
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