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Rolling icosahedron footprints: number of 4Xn 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge
1

%I #4 Mar 19 2013 11:32:52

%S 1728,78125,6865625,603351125,54279694625,4903804407125,

%T 443803619416625,40180564679055125,3638107937069854625,

%U 329414029399378035125,29827030198435983748625,2700711676390250182863125

%N Rolling icosahedron footprints: number of 4Xn 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge

%C Row 4 of A223321

%H R. H. Hardin, <a href="/A223324/b223324.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 121*a(n-1) -3029*a(n-2) +25559*a(n-3) -89707*a(n-4) +122263*a(n-5) -12831*a(n-6) -60039*a(n-7) for n>10

%e Some solutions for n=3

%e ..0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0

%e ..0..5..7....0..1..3....0..1..8....0..6.10....0..7.11....0..6..5....0..1..2

%e ..0..5..6....3..8..2....2..1..3....4..9..8...11..7..0....2..0..2....0..6..0

%e .10..5..0....4..6..2....3..9.11....8..4..6....1..2..0....2..8..1....0..1..3

%e Vertex neighbors:

%e 0 -> 1 2 5 6 7

%e 1 -> 0 2 3 7 8

%e 2 -> 0 1 4 6 8

%e 3 -> 1 7 8 9 11

%e 4 -> 2 6 8 9 10

%e 5 -> 0 6 7 10 11

%e 6 -> 0 2 4 5 10

%e 7 -> 0 1 3 5 11

%e 8 -> 1 2 3 4 9

%e 9 -> 3 4 8 10 11

%e 10 -> 4 5 6 9 11

%e 11 -> 3 5 7 9 10

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 19 2013