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A223277 Rolling icosahedron face footprints: number of n X 3 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

%I A223277 #7 Aug 18 2018 08:42:44
%S A223277 9,87,849,8295,81057,792087,7740273,75637959,739134273,7222821495,
%T A223277 70581425169,689721818919,6739962906081,65862930139863,
%U A223277 643612676665521,6289384281642375,61459874978079873,600586013379170103
%N A223277 Rolling icosahedron face footprints: number of n X 3 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.
%C A223277 Column 3 of A223282.
%H A223277 R. H. Hardin, <a href="/A223277/b223277.txt">Table of n, a(n) for n = 1..210</a>
%F A223277 Empirical: a(n) = 11*a(n-1) - 12*a(n-2).
%F A223277 Conjectures from _Colin Barker_, Aug 18 2018: (Start)
%F A223277 G.f.: 3*x*(3 - 4*x) / (1 - 11*x + 12*x^2).
%F A223277 a(n) = (2^(-1-n)*((11-sqrt(73))^n*(-7+sqrt(73)) + (7+sqrt(73))*(11+sqrt(73))^n)) / sqrt(73).
%F A223277 (End)
%e A223277 Some solutions for n=3:
%e A223277 ..0..2..3....0..2..3....0..1..4....0..5..9....0..1..6....0..2..0....0..5..9
%e A223277 ..0..2..3....8..2..3....0..1..4....0..5..0....0..1..0....3..2..8....9..5..9
%e A223277 ..0..2..8....0..2..8....0..1..4....0..1..0....4..1..4....3..2..8....0..5..7
%e A223277 Face neighbors:
%e A223277 0 -> 1 2 5
%e A223277 1 -> 0 4 6
%e A223277 2 -> 0 3 8
%e A223277 3 -> 2 4 16
%e A223277 4 -> 3 1 17
%e A223277 5 -> 0 7 9
%e A223277 6 -> 1 7 10
%e A223277 7 -> 6 5 11
%e A223277 8 -> 2 9 13
%e A223277 9 -> 8 5 14
%e A223277 10 -> 6 12 17
%e A223277 11 -> 7 12 14
%e A223277 12 -> 11 10 19
%e A223277 13 -> 8 15 16
%e A223277 14 -> 9 11 15
%e A223277 15 -> 14 13 19
%e A223277 16 -> 3 13 18
%e A223277 17 -> 4 10 18
%e A223277 18 -> 16 17 19
%e A223277 19 -> 15 18 12
%Y A223277 Cf. A223282.
%K A223277 nonn
%O A223277 1,1
%A A223277 _R. H. Hardin_, Mar 19 2013