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A223207 Rolling icosahedron face footprints: number of nX6 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 A223207 #6 Jul 23 2025 03:51:39
%S A223207 243,9375,443451,22163655,1127761923,57728430255,2960941376139,
%T A223207 151970441720919,7801619707803603,400536865551609279,
%U A223207 20564155823714361819,1055802848340690163431,54207072655600127312547
%N A223207 Rolling icosahedron face footprints: number of nX6 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 A223207 Column 6 of A223209
%H A223207 R. H. Hardin, <a href="/A223207/b223207.txt">Table of n, a(n) for n = 1..210</a>
%F A223207 Empirical: a(n) = 77*a(n-1) -1444*a(n-2) +5860*a(n-3) +38744*a(n-4) -300016*a(n-5) +339296*a(n-6) +1286720*a(n-7) -2655360*a(n-8) -56832*a(n-9) +1682944*a(n-10) -149504*a(n-11) -163840*a(n-12)
%e A223207 Some solutions for n=3
%e A223207 ..0..2..0..1..6.10....0..1..6.10..6.10....0..5..0..2..3..4....0..5..9..5..9..8
%e A223207 ..5..0..1..0..1..6....5..0..1..6..1..6....5..0..2..3.16..3....5..9..5..9..8..9
%e A223207 ..0..2..0..1..6.10....0..1..4..1..6..1....0..2..3..2..3.16....0..5..0..5..9.14
%e A223207 Face neighbors:
%e A223207 0 -> 1 2 5
%e A223207 1 -> 0 4 6
%e A223207 2 -> 0 3 8
%e A223207 3 -> 2 4 16
%e A223207 4 -> 3 1 17
%e A223207 5 -> 0 7 9
%e A223207 6 -> 1 7 10
%e A223207 7 -> 6 5 11
%e A223207 8 -> 2 9 13
%e A223207 9 -> 8 5 14
%e A223207 10 -> 6 12 17
%e A223207 11 -> 7 12 14
%e A223207 12 -> 11 10 19
%e A223207 13 -> 8 15 16
%e A223207 14 -> 9 11 15
%e A223207 15 -> 14 13 19
%e A223207 16 -> 3 13 18
%e A223207 17 -> 4 10 18
%e A223207 18 -> 16 17 19
%e A223207 19 -> 15 18 12
%K A223207 nonn
%O A223207 1,1
%A A223207 _R. H. Hardin_ Mar 18 2013