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A223280 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, diagonal or antidiagonal neighbor moves across an icosahedral edge.

%I A223280 #6 Jul 23 2025 03:57:12
%S A223280 243,6831,261819,10979127,473368227,20570223999,895927195659,
%T A223280 39047604482055,1702160040384051,74204651599582287,
%U A223280 3234961829070975771,141029297731894387287,6148230806876335875267,268034791871130540563487
%N A223280 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, diagonal or antidiagonal neighbor moves across an icosahedral edge.
%C A223280 Column 6 of A223282
%H A223280 R. H. Hardin, <a href="/A223280/b223280.txt">Table of n, a(n) for n = 1..210</a>
%F A223280 Empirical: a(n) = 63*a(n-1) -882*a(n-2) +792*a(n-3) +35736*a(n-4) -70768*a(n-5) -246208*a(n-6) +327936*a(n-7) +146432*a(n-8) -180224*a(n-9)
%e A223280 Some solutions for n=3
%e A223280 ..0..2..3..2..3..2....0..5..0..1..0..1....0..5..0..5..0..5....0..2..0..1..4..1
%e A223280 ..0..2..8..2..8..2....0..5..0..2..0..2....0..5..0..2..0..1....0..2..0..1..0..1
%e A223280 ..8..2..0..2..8.13....0..5..0..2..3..2....7..5..0..2..0..5....0..1..0..1..6..1
%e A223280 Face neighbors:
%e A223280 0 -> 1 2 5
%e A223280 1 -> 0 4 6
%e A223280 2 -> 0 3 8
%e A223280 3 -> 2 4 16
%e A223280 4 -> 3 1 17
%e A223280 5 -> 0 7 9
%e A223280 6 -> 1 7 10
%e A223280 7 -> 6 5 11
%e A223280 8 -> 2 9 13
%e A223280 9 -> 8 5 14
%e A223280 10 -> 6 12 17
%e A223280 11 -> 7 12 14
%e A223280 12 -> 11 10 19
%e A223280 13 -> 8 15 16
%e A223280 14 -> 9 11 15
%e A223280 15 -> 14 13 19
%e A223280 16 -> 3 13 18
%e A223280 17 -> 4 10 18
%e A223280 18 -> 16 17 19
%e A223280 19 -> 15 18 12
%K A223280 nonn
%O A223280 1,1
%A A223280 _R. H. Hardin_ Mar 19 2013