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A223286 Rolling icosahedron face footprints: number of 5Xn 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 A223286 #6 Jul 23 2025 03:57:32
%S A223286 160000,1875,81057,1048923,28271577,473368227,10801441521,
%T A223286 200475062187,4265203621833,82829709506163,1709099202398433,
%U A223286 33866115603026427,689396112362771001,13783610690189186115,278907343566603743697
%N A223286 Rolling icosahedron face footprints: number of 5Xn 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 A223286 Row 5 of A223282
%H A223286 R. H. Hardin, <a href="/A223286/b223286.txt">Table of n, a(n) for n = 1..210</a>
%F A223286 Empirical: a(n) = 13*a(n-1) +278*a(n-2) -2372*a(n-3) -11584*a(n-4) +98256*a(n-5) +68096*a(n-6) -1208064*a(n-7) +753664*a(n-8) +4509696*a(n-9) -4485120*a(n-10) -4571136*a(n-11) +4718592*a(n-12) for n>13
%e A223286 Some solutions for n=3
%e A223286 ..0..1..4....0..2..0....0..2..8....0..5..9....0..5..0....0..2..3....0..1..6
%e A223286 ..4..1..0....0..5..0....0..2..0....0..5..0....0..1..0....0..2..8....4..1..4
%e A223286 ..6..1..6....9..5..9....3..2..0....0..1..0....6..1..0....8..2..3....4..1..6
%e A223286 ..6..7..6....9..8..9....8..2..3....4..1..0....0..1..4....3..2..3....6..1..4
%e A223286 .11..7.11...13..8..2....8..2..3....0..1..6....4..1..6....3..4..3....6..1..4
%e A223286 Face neighbors:
%e A223286 0 -> 1 2 5
%e A223286 1 -> 0 4 6
%e A223286 2 -> 0 3 8
%e A223286 3 -> 2 4 16
%e A223286 4 -> 3 1 17
%e A223286 5 -> 0 7 9
%e A223286 6 -> 1 7 10
%e A223286 7 -> 6 5 11
%e A223286 8 -> 2 9 13
%e A223286 9 -> 8 5 14
%e A223286 10 -> 6 12 17
%e A223286 11 -> 7 12 14
%e A223286 12 -> 11 10 19
%e A223286 13 -> 8 15 16
%e A223286 14 -> 9 11 15
%e A223286 15 -> 14 13 19
%e A223286 16 -> 3 13 18
%e A223286 17 -> 4 10 18
%e A223286 18 -> 16 17 19
%e A223286 19 -> 15 18 12
%K A223286 nonn
%O A223286 1,1
%A A223286 _R. H. Hardin_ Mar 19 2013