A223397 - OEIS

%I #4 Mar 19 2013 18:13:49

%S 152,2360,39480,672784,11561512,199425400,3445747472,59582558136,

%T 1030635314552,17830297764560,308491144480488,5337532888545800,

%U 92351643563233552,1597906958454938296,27647738113504778888

%N 4X4 square grid graph coloring a rectangular array: number of nX3 0..15 arrays where 0..15 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 A223402

%H R. H. Hardin, <a href="/A223397/b223397.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 18*a(n-1) +69*a(n-2) -1554*a(n-3) +2085*a(n-4) +10353*a(n-5) -18959*a(n-6) -11633*a(n-7) +31508*a(n-8) -5302*a(n-9) -10390*a(n-10) +4408*a(n-11) -440*a(n-12) for n>13

%e Some solutions for n=3

%e ..5..1..2....5..4..5....3..7..6....6.10.14....5..9.10....7..6..5...10..9..8

%e ..6..2..3....6..5..1....7.11.10...10.14.10....6..5..6...11.10..9....9.10..9

%e ..5..1..2....2..1..2...11.10.14....6.10..6....2..1..5....7..6.10...10.11.10

%e Vertex neighbors:

%e 0 -> 1 4

%e 1 -> 0 2 5

%e 2 -> 1 3 6

%e 3 -> 2 7

%e 4 -> 0 5 8

%e 5 -> 4 1 6 9

%e 6 -> 5 2 7 10

%e 7 -> 6 3 11

%e 8 -> 4 9 12

%e 9 -> 8 5 10 13

%e 10 -> 9 6 11 14

%e 11 -> 10 7 15

%e 12 -> 8 13

%e 13 -> 12 9 14

%e 14 -> 13 10 15

%e 15 -> 14 11

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 19 2013