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A223206 Rolling icosahedron face footprints: number of nX5 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or vertical neighbor moves across an icosahedral edge.

%I A223206 #6 Jul 23 2025 03:51:32
%S A223206 81,1875,50553,1412907,39868737,1127761923,31921015497,903661481115,
%T A223206 25583075832465,724276345970163,20504869741550745,580510427181846027,
%U A223206 16434750355138945761,465281963351360897763,13172534004090254190441
%N A223206 Rolling icosahedron face footprints: number of nX5 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or vertical neighbor moves across an icosahedral edge.
%C A223206 Column 5 of A223209
%H A223206 R. H. Hardin, <a href="/A223206/b223206.txt">Table of n, a(n) for n = 1..210</a>
%F A223206 Empirical: a(n) = 31*a(n-1) -24*a(n-2) -1612*a(n-3) +3816*a(n-4) +1152*a(n-5) -2784*a(n-6) +256*a(n-7)
%e A223206 Some solutions for n=3
%e A223206 ..0..1..4..3..4....0..2..0..2..0....0..1..0..2..3....0..2..0..1..6
%e A223206 ..1..4..3..4..1....2..8..2..0..2....5..0..5..0..2....1..0..1..4..1
%e A223206 ..4..1..4..1..6....8..2..3..2..3....0..2..0..5..0....0..1..4..1..4
%e A223206 Face neighbors:
%e A223206 0 -> 1 2 5
%e A223206 1 -> 0 4 6
%e A223206 2 -> 0 3 8
%e A223206 3 -> 2 4 16
%e A223206 4 -> 3 1 17
%e A223206 5 -> 0 7 9
%e A223206 6 -> 1 7 10
%e A223206 7 -> 6 5 11
%e A223206 8 -> 2 9 13
%e A223206 9 -> 8 5 14
%e A223206 10 -> 6 12 17
%e A223206 11 -> 7 12 14
%e A223206 12 -> 11 10 19
%e A223206 13 -> 8 15 16
%e A223206 14 -> 9 11 15
%e A223206 15 -> 14 13 19
%e A223206 16 -> 3 13 18
%e A223206 17 -> 4 10 18
%e A223206 18 -> 16 17 19
%e A223206 19 -> 15 18 12
%K A223206 nonn
%O A223206 1,1
%A A223206 _R. H. Hardin_ Mar 18 2013