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A223324 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.

%I A223324 #6 Jul 23 2025 04:00:29
%S A223324 1728,78125,6865625,603351125,54279694625,4903804407125,
%T A223324 443803619416625,40180564679055125,3638107937069854625,
%U A223324 329414029399378035125,29827030198435983748625,2700711676390250182863125
%N A223324 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 A223324 Row 4 of A223321
%H A223324 R. H. Hardin, <a href="/A223324/b223324.txt">Table of n, a(n) for n = 1..210</a>
%F A223324 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 A223324 Some solutions for n=3
%e A223324 ..0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0
%e A223324 ..0..5..7....0..1..3....0..1..8....0..6.10....0..7.11....0..6..5....0..1..2
%e A223324 ..0..5..6....3..8..2....2..1..3....4..9..8...11..7..0....2..0..2....0..6..0
%e A223324 .10..5..0....4..6..2....3..9.11....8..4..6....1..2..0....2..8..1....0..1..3
%e A223324 Vertex neighbors:
%e A223324 0 -> 1 2 5 6 7
%e A223324 1 -> 0 2 3 7 8
%e A223324 2 -> 0 1 4 6 8
%e A223324 3 -> 1 7 8 9 11
%e A223324 4 -> 2 6 8 9 10
%e A223324 5 -> 0 6 7 10 11
%e A223324 6 -> 0 2 4 5 10
%e A223324 7 -> 0 1 3 5 11
%e A223324 8 -> 1 2 3 4 9
%e A223324 9 -> 3 4 8 10 11
%e A223324 10 -> 4 5 6 9 11
%e A223324 11 -> 3 5 7 9 10
%K A223324 nonn
%O A223324 1,1
%A A223324 _R. H. Hardin_ Mar 19 2013