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A223477 Rolling icosahedron face footprints: number of n X 5 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves across an icosahedral edge.

%I A223477 #8 Aug 20 2018 13:30:45
%S A223477 81,3375,147825,6526575,288507825,12755926575,563999907825,
%T A223477 24937217326575,1102598111307825,48751338478726575,
%U A223477 2155538829022707825,95307078736540126575,4213999366856734107825,186321844088731401526575
%N A223477 Rolling icosahedron face footprints: number of n X 5 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves across an icosahedral edge.
%C A223477 Column 5 of A223480.
%H A223477 R. H. Hardin, <a href="/A223477/b223477.txt">Table of n, a(n) for n = 1..210</a>
%F A223477 Empirical: a(n) = 51*a(n-1) - 300*a(n-2).
%F A223477 Empirical g.f.: 27*x*(3 - 28*x) / (1 - 51*x + 300*x^2). - _Colin Barker_, Aug 20 2018
%e A223477 Some solutions for n=3:
%e A223477 ..0..1..6.10.17....0..1..6..7..5....0..2..0..2..0....0..2..0..1..6
%e A223477 ..6.10.17.10.12....6..7.11..7..6....8..2..0..5..7....0..1..0..1..4
%e A223477 .17.10.12.11.12....6..7..5..7..5....0..5..7.11.14....0..5..0..1..6
%e A223477 Face neighbors:
%e A223477 0 -> 1 2 5
%e A223477 1 -> 0 4 6
%e A223477 2 -> 0 3 8
%e A223477 3 -> 2 4 16
%e A223477 4 -> 3 1 17
%e A223477 5 -> 0 7 9
%e A223477 6 -> 1 7 10
%e A223477 7 -> 6 5 11
%e A223477 8 -> 2 9 13
%e A223477 9 -> 8 5 14
%e A223477 10 -> 6 12 17
%e A223477 11 -> 7 12 14
%e A223477 12 -> 11 10 19
%e A223477 13 -> 8 15 16
%e A223477 14 -> 9 11 15
%e A223477 15 -> 14 13 19
%e A223477 16 -> 3 13 18
%e A223477 17 -> 4 10 18
%e A223477 18 -> 16 17 19
%e A223477 19 -> 15 18 12
%Y A223477 Cf. A223480.
%K A223477 nonn
%O A223477 1,1
%A A223477 _R. H. Hardin_, Mar 20 2013