A223409 - OEIS

A223409

4 X 4 X 4 triangular graph without horizontal edges coloring a rectangular array: number of n X 2 0..9 arrays where 0..9 label nodes of a graph with edges 0,1 0,2 1,3 1,4 2,4 2,5 3,6 3,7 4,7 4,8 5,8 5,9 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

%I #7 Aug 20 2018 08:49:44

%S 24,132,780,4664,28060,169124,1020056,6153860,37128748,224020376,

%T 1351668764,8155585924,49208586616,296911448452,1791484795980,

%U 10809344595640,65220724455836,393524597542756,2374423335359192

%N 4 X 4 X 4 triangular graph without horizontal edges coloring a rectangular array: number of n X 2 0..9 arrays where 0..9 label nodes of a graph with edges 0,1 0,2 1,3 1,4 2,4 2,5 3,6 3,7 4,7 4,8 5,8 5,9 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

%C Column 2 of A223415.

%H R. H. Hardin, <a href="/A223409/b223409.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) - 17*a(n-2) - 10*a(n-3) + 26*a(n-4) + 10*a(n-5).

%F Empirical g.f.: 4*x*(6 - 21*x + 32*x^3 + 10*x^4) / (1 - 9*x + 17*x^2 + 10*x^3 - 26*x^4 - 10*x^5). - _Colin Barker_, Aug 20 2018

%e Some solutions for n=3:

%e ..5..2....2..0....4..1....3..1....6..3....8..5....8..5....4..2....1..4....2..4

%e ..8..4....0..1....7..4....1..0....3..1....4..8....4..2....8..4....0..2....4..8

%e ..4..7....1..4....4..1....0..1....6..3....1..4....8..4....5..2....2..5....1..4

%Y Cf. A223415.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 20 2013