A223337 - OEIS

A223337

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

%I #9 Aug 19 2018 16:42:42

%S 15,60,264,1176,5280,23712,106560,478848,2151936,9670656,43459584,

%T 195305472,877694976,3944325120,17725636608,79658287104,357981093888,

%U 1608752431104,7229667803136,32489832185856,146007980507136

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

%C Column 1 of A223344.

%H R. H. Hardin, <a href="/A223337/b223337.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + 4*a(n-2) - 8*a(n-3).

%F Empirical g.f.: 3*x*(5 - 12*x^2) / (1 - 4*x - 4*x^2 + 8*x^3). - _Colin Barker_, Aug 19 2018

%e Some solutions for n=3:

%e ..3...11...11....9....4...11....4....5...10....6....8....7....2....8....4....8

%e ..7....7...10....8....7....7....5....8....6....7....4....4....4....9....2...12

%e ..3....8....6....7....3....6....8...12....3....6....7....7....7....5....5...11

%Y Cf. A223344.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 19 2013