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%I #6 Apr 12 2023 08:02:30
%S 3200000,9375,792087,15229647,792881031,20570223999,879050854455,
%T 26073158735535,1008694505830119,32094483162308319,
%U 1178050642133703831,38926413103761206799,1389205962179205980487,46849778740107421135935
%N Rolling icosahedron face footprints: number of 6 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 6 of A223282.
%H R. H. Hardin, <a href="/A223287/b223287.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 13*a(n-1) +1244*a(n-2) -8256*a(n-3) -402464*a(n-4) +1780288*a(n-5) +55907168*a(n-6) -197740288*a(n-7) -4040907520*a(n-8) +12437493760*a(n-9) +166070886400*a(n-10) -452922138624*a(n-11) -4093663121408*a(n-12) +9761715879936*a(n-13) +62363887337472*a(n-14) -126220206735360*a(n-15) -595038449696768*a(n-16) +978337484767232*a(n-17) +3542610027216896*a(n-18) -4455273209004032*a(n-19) -12803732509032448*a(n-20) +11344509988241408*a(n-21) +26381276122447872*a(n-22) -14571020149063680*a(n-23) -27374953313599488*a(n-24) +7085252929388544*a(n-25) +10449758510383104*a(n-26) for n>27.
%e Some solutions for n=3
%e ..0..5..0....0..5..0....0..5..0....0..5..0....0..5..0....0..5..0....0..5..0
%e ..0..5..9....7..5..9....0..5..0....7..5..9....9..5..9....0..5..9....9..5..7
%e ..7..5..0....7..5..7....9..5..9....0..5..7....7..5..0....7..5..0....9..5..7
%e ..0..5..9....0..5..9....9..5..9....9..5..9....9..5..0....9..5..9....7..5..0
%e ..9..5..0....7..5..0....9..8..9....9..5..0....7..5..0....9.14..9....7..5..7
%e ..9..5..9....0..5..9...13..8..2....7..5..9....7..5..7...11.14..9....7..5..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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