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%I #9 Aug 18 2018 15:44:23
%S 8000,375,8295,72279,1024071,10979127,137621799,1576368663,
%T 19009505799,222545715447,2650002132711,31248496329687,
%U 370552575553479,4379948164268727,51867287743753383,613557282050858391
%N Rolling icosahedron face footprints: number of 4 X n 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 Row 4 of A223282.
%H R. H. Hardin, <a href="/A223285/b223285.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) + 92*a(n-2) - 56*a(n-3) - 920*a(n-4) + 192*a(n-5) + 1152*a(n-6) for n>7.
%F Empirical g.f.: x*(8000 - 39625*x - 729580*x^2 + 444304*x^3 + 7280536*x^4 - 1517376*x^5 - 9097344*x^6) / (1 - 5*x - 92*x^2 + 56*x^3 + 920*x^4 - 192*x^5 - 1152*x^6). - _Colin Barker_, Aug 18 2018
%e Some solutions for n=3:
%e 0 1 0 0 2 0 0 2 8 0 5 7 0 1 4 0 2 3 0 1 4
%e 4 1 4 0 2 8 8 2 3 9 5 9 4 1 0 8 2 0 6 1 6
%e 6 1 4 0 2 3 0 2 8 9 5 0 0 1 6 0 2 8 6 1 6
%e 6 1 0 8 2 8 3 2 0 9 5 0 6 1 6 0 2 8 4 1 0
%e Face neighbors:
%e 0 -> 1 2 5
%e 1 -> 0 4 6
%e 2 -> 0 3 8
%e 3 -> 2 4 16
%e 4 -> 3 1 17
%e 5 -> 0 7 9
%e 6 -> 1 7 10
%e 7 -> 6 5 11
%e 8 -> 2 9 13
%e 9 -> 8 5 14
%e 10 -> 6 12 17
%e 11 -> 7 12 14
%e 12 -> 11 10 19
%e 13 -> 8 15 16
%e 14 -> 9 11 15
%e 15 -> 14 13 19
%e 16 -> 3 13 18
%e 17 -> 4 10 18
%e 18 -> 16 17 19
%e 19 -> 15 18 12
%Y Cf. A223282.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 19 2013
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