A223693 - OEIS

A223693

Petersen graph (8,2) coloring a rectangular array: number of 2 X n 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph.

%I #8 Aug 22 2018 18:04:35

%S 256,432,2304,12384,66816,361440,1958400,10622304,57652992,313044192,

%T 1700213760,9235776096,50175150336,272604245472,1481134892544,

%U 8047630034784,43726888532736,237593019598560,1290986302371840

%N Petersen graph (8,2) coloring a rectangular array: number of 2 X n 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph.

%C Row 2 of A223692.

%H R. H. Hardin, <a href="/A223693/b223693.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) - 11*a(n-2) - 16*a(n-3) for n>4.

%F Empirical g.f.: 16*x*(16 - 101*x + 104*x^2 + 175*x^3) / (1 - 8*x + 11*x^2 + 16*x^3). - _Colin Barker_, Aug 22 2018

%e Some solutions for n=3:

%e ..2.10..2....6.14.12....6..7..0...13.11..3....4..5..6....1..9..1...11.13..5

%e ..2..3.11....8.10..2....6..7..0....3.11.13....4..5.13....1..0..8....5..4..3

%Y Cf. A223692.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 25 2013