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A223479 Rolling icosahedron face footprints: number of nX7 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves across an icosahedral edge.

%I A223479 #6 Jul 23 2025 04:12:27
%S A223479 729,84375,11374425,1588785975,223894186425,31621425535575,
%T A223479 4468456626780825,631526586023769975,89256484380983132025,
%U A223479 12615117535169199386775,1782968370270784918644825
%N A223479 Rolling icosahedron face footprints: number of nX7 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves across an icosahedral edge.
%C A223479 Column 7 of A223480
%H A223479 R. H. Hardin, <a href="/A223479/b223479.txt">Table of n, a(n) for n = 1..210</a>
%F A223479 Empirical: a(n) = 227*a(n-1) -14764*a(n-2) +411840*a(n-3) -5347200*a(n-4) +29600000*a(n-5) -48000000*a(n-6)
%e A223479 Some solutions for n=3
%e A223479 ..0..5..0..5..7.11..7....0..5..0..1..4..1..6....0..5..0..5..0..2..0
%e A223479 ..0..5..0..5..7..5..9....0..5..0..1..6..1..0....0..5..0..1..0..2..8
%e A223479 ..0..5..9..5..9..5..7....0..1..0..1..0..5..0....0..1..4..1..0..2..0
%e A223479 Face neighbors:
%e A223479 0 -> 1 2 5
%e A223479 1 -> 0 4 6
%e A223479 2 -> 0 3 8
%e A223479 3 -> 2 4 16
%e A223479 4 -> 3 1 17
%e A223479 5 -> 0 7 9
%e A223479 6 -> 1 7 10
%e A223479 7 -> 6 5 11
%e A223479 8 -> 2 9 13
%e A223479 9 -> 8 5 14
%e A223479 10 -> 6 12 17
%e A223479 11 -> 7 12 14
%e A223479 12 -> 11 10 19
%e A223479 13 -> 8 15 16
%e A223479 14 -> 9 11 15
%e A223479 15 -> 14 13 19
%e A223479 16 -> 3 13 18
%e A223479 17 -> 4 10 18
%e A223479 18 -> 16 17 19
%e A223479 19 -> 15 18 12
%K A223479 nonn
%O A223479 1,1
%A A223479 _R. H. Hardin_ Mar 20 2013