A223396 - OEIS

%I #7 Aug 20 2018 08:37:46

%S 48,328,2360,17280,127464,943016,6985008,51763176,383669400,

%T 2843977792,21081830152,156277203016,1158470626096,8587668090888,

%U 63659878472312,471907077858304,3498220894515624,25932117973637736,192233359691316016

%N 4 X 4 square grid graph coloring a rectangular array: number of n X 2 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 2 of A223402.

%H R. H. Hardin, <a href="/A223396/b223396.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) - 18*a(n-2) - 9*a(n-3) + 2*a(n-4).

%F Empirical g.f.: 8*x*(2 + x)*(3 - 11*x + 2*x^2) / (1 - 10*x + 18*x^2 + 9*x^3 - 2*x^4). - _Colin Barker_, Aug 20 2018

%e Some solutions for n=3:

%e ..6.10...10.14...13.14....9.13....8..9....6..2....9..5....9.13....3..7....5..1

%e .10..6...14.10....9.10...13..9....4..8....7..3...13..9...10.14....2..6....4..5

%e .14.10...10.14...10.11....9.10....8..9...11..7....9..5...14.15....6..2....0..4

%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

%Y Cf. A223402.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 19 2013