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A223234 Rolling icosahedron footprints: number of 2 X n 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an icosahedral edge.

%I A223234 #7 Aug 17 2018 09:22:44
%S A223234 12,65,785,7445,75665,753005,7540985,75377045,753868865,7538393405,
%T A223234 75384819785,753845540645,7538463378065,75384609865805,
%U A223234 753846170402585,7538461488792245,75384615533623265,753846153399130205
%N A223234 Rolling icosahedron footprints: number of 2 X n 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an icosahedral edge.
%C A223234 Row 2 of A223233.
%H A223234 R. H. Hardin, <a href="/A223234/b223234.txt">Table of n, a(n) for n = 1..210</a>
%F A223234 Empirical: a(n) = 7*a(n-1) + 30*a(n-2) for n>3.
%F A223234 Conjectures from _Colin Barker_, Aug 17 2018: (Start)
%F A223234 G.f.: x*(12 - 19*x - 30*x^2) / ((1 + 3*x)*(1 - 10*x)).
%F A223234 a(n) = (-25*(-1)^n*3^(1+n) + 49*10^n) / 65 for n>1.
%F A223234 (End)
%e A223234 Some solutions for n=3:
%e A223234 ..0..2..1....0..7.11....0..6..2....0..6..5....0..7..3....0..2..1....0..2..0
%e A223234 ..0..7..0....3..7..3...10..6..4....4..6..5....3..7..0....6..2..8....8..2..4
%e A223234 Vertex neighbors:
%e A223234 0 -> 1 2 5 6 7
%e A223234 1 -> 0 2 3 7 8
%e A223234 2 -> 0 1 4 6 8
%e A223234 3 -> 1 7 8 9 11
%e A223234 4 -> 2 6 8 9 10
%e A223234 5 -> 0 6 7 10 11
%e A223234 6 -> 0 2 4 5 10
%e A223234 7 -> 0 1 3 5 11
%e A223234 8 -> 1 2 3 4 9
%e A223234 9 -> 3 4 8 10 11
%e A223234 10 -> 4 5 6 9 11
%e A223234 11 -> 3 5 7 9 10
%Y A223234 Cf. A223233.
%K A223234 nonn
%O A223234 1,1
%A A223234 _R. H. Hardin_, Mar 18 2013