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%I
%S 68,912,13232,192752,2812608,41044048,598980512,8741293936,
%T 127567402912,1861673117136,27168612726112,396489050362864,
%U 5786223905786400,84442089417201488,1232318612693585248,17984018624753407088
%N 3 X 3 square grid graph coloring a rectangular array: number of n X 3 0..8 arrays where 0..8 label nodes of the square grid graph and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
%C Column 3 of A223379.
%H R. H. Hardin, <a href="/A223374/b223374.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 221*a(n-2) - 1718*a(n-4) + 1872*a(n-6) for n>7.
%F Empirical g.f.: 4*x*(17 + 228*x - 449*x^2 - 2200*x^3 + 1290*x^4 + 3168*x^5 - 144*x^6) / (1 - 221*x^2 + 1718*x^4 - 1872*x^6). - _Colin Barker_, Aug 20 2018
%e Some solutions for n=3:
%e ..1..4..7....6..7..6....5..8..7....7..4..3....3..4..7....8..5..4....8..7..6
%e ..4..7..4....7..6..3....4..7..4....4..3..4....4..7..4....5..4..7....7..6..3
%e ..7..8..5....6..3..6....3..4..7....3..4..5....5..8..5....2..5..8....4..7..6
%e Vertex neighbors:
%e 0 -> 1 3
%e 1 -> 0 2 4
%e 2 -> 1 5
%e 3 -> 0 4 6
%e 4 -> 3 1 5 7
%e 5 -> 4 2 8
%e 6 -> 3 7
%e 7 -> 6 4 8
%e 8 -> 7 5
%Y Cf. A223379.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 19 2013
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