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A223182 Rolling icosahedron footprints: number of n X 4 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, vertical or antidiagonal neighbor moves along an icosahedral edge.

%I A223182 #8 Aug 17 2018 09:21:53
%S A223182 125,320,2080,14560,103520,738720,5274720,37664800,268947680,
%T A223182 1920431520,13712917600,97917648160,699184991200,4992559175840,
%U A223182 35649574015840,254557248560160,1817676496339680,12979193733707680,92678466337073760
%N A223182 Rolling icosahedron footprints: number of n X 4 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, vertical or antidiagonal neighbor moves along an icosahedral edge.
%C A223182 Column 4 of A223186.
%H A223182 R. H. Hardin, <a href="/A223182/b223182.txt">Table of n, a(n) for n = 1..210</a>
%F A223182 Empirical: a(n) = 10*a(n-1) - 25*a(n-2) + 36*a(n-3) - 24*a(n-4) + 4*a(n-5) for n>6.
%F A223182 Empirical g.f.: 5*x*(25 - 186*x + 401*x^2 - 548*x^3 + 280*x^4 - 36*x^5) / ((1 - x)*(1 - 9*x + 16*x^2 - 20*x^3 + 4*x^4)). - _Colin Barker_, Aug 17 2018
%e A223182 Some solutions for n=3:
%e A223182 ..0..5..7.11....0..5.10.11....0..5..7..0....0..6..2..0....0..5.10.11
%e A223182 ..7.11..3..7....7.11..5.10....7.11..5..7....2..0..1..7....7.11..9.10
%e A223182 ..5..7..1..3....5..7.11..5....3..7..0..5....1..7..0..1....5.10..4..9
%e A223182 Vertex neighbors:
%e A223182 0 -> 1 2 5 6 7
%e A223182 1 -> 0 2 3 7 8
%e A223182 2 -> 0 1 4 6 8
%e A223182 3 -> 1 7 8 9 11
%e A223182 4 -> 2 6 8 9 10
%e A223182 5 -> 0 6 7 10 11
%e A223182 6 -> 0 2 4 5 10
%e A223182 7 -> 0 1 3 5 11
%e A223182 8 -> 1 2 3 4 9
%e A223182 9 -> 3 4 8 10 11
%e A223182 10 -> 4 5 6 9 11
%e A223182 11 -> 3 5 7 9 10
%Y A223182 Cf. A223186.
%K A223182 nonn
%O A223182 1,1
%A A223182 _R. H. Hardin_, Mar 18 2013