%I #8 Aug 21 2018 05:54:46

%S 36,121,1519,16323,182901,2030665,22598167,251348043,2795984857,

%T 31101456601,345963177427,3848382739711,42808185822221,

%U 476184598157809,5296925638013539,58921311528252323,655421879453116645

%N Petersen graph (3,1) coloring a rectangular array: number of 3 X n 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

%C Row 3 of A223504.

%H R. H. Hardin, <a href="/A223506/b223506.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 12*a(n-1) - 4*a(n-2) - 73*a(n-3) + 103*a(n-4) - 23*a(n-5) - 16*a(n-6) + 4*a(n-7) for n>8.

%F Empirical g.f.: x*(36 - 311*x + 211*x^2 + 1207*x^3 - 1774*x^4 + 397*x^5 + 272*x^6 - 68*x^7) / (1 - 12*x + 4*x^2 + 73*x^3 - 103*x^4 + 23*x^5 + 16*x^6 - 4*x^7). - _Colin Barker_, Aug 21 2018

%e Some solutions for n=3:

%e ..0..2..5....0..3..4....0..1..0....0..2..1....0..3..0....0..3..0....0..1..4

%e ..1..2..1....0..3..5....4..1..4....0..2..1....5..2..0....4..1..0....4..3..4

%e ..5..4..1....5..3..5....4..3..0....1..2..1....0..2..5....4..3..0....0..1..0

%Y Cf. A223504.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 21 2013