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A223322 Rolling icosahedron footprints: number of 2 X n 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.

%I A223322 #9 Jun 29 2023 11:16:29
%S A223322 12,125,1625,21125,274625,3570125,46411625,603351125,7843564625,
%T A223322 101966340125,1325562421625,17232311481125,224020049254625,
%U A223322 2912260640310125,37859388324031625,492172048212411125
%N A223322 Rolling icosahedron footprints: number of 2 X n 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.
%C A223322 Row 2 of A223321.
%H A223322 R. H. Hardin, <a href="/A223322/b223322.txt">Table of n, a(n) for n = 1..210</a>
%H A223322 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (13).
%F A223322 Empirical: a(n) = 13*a(n-1) for n>2.
%F A223322 Conjectures from _Colin Barker_, Aug 19 2018: (Start)
%F A223322 G.f.: x*(12 - 31*x) / (1 - 13*x).
%F A223322 a(n) = 125*13^(n-2) for n>1.
%F A223322 (End)
%e A223322 Some solutions for n=3:
%e A223322 ..0..7..3....0..2..8....0..2..4....0..5.11....0..6..5....0..1..3....0..7..0
%e A223322 ..1..8..4....8..1..2....8..2..1...10..9..4....2..6..2....3.11..3....0..1..7
%e A223322 Vertex neighbors:
%e A223322 0 -> 1 2 5 6 7
%e A223322 1 -> 0 2 3 7 8
%e A223322 2 -> 0 1 4 6 8
%e A223322 3 -> 1 7 8 9 11
%e A223322 4 -> 2 6 8 9 10
%e A223322 5 -> 0 6 7 10 11
%e A223322 6 -> 0 2 4 5 10
%e A223322 7 -> 0 1 3 5 11
%e A223322 8 -> 1 2 3 4 9
%e A223322 9 -> 3 4 8 10 11
%e A223322 10 -> 4 5 6 9 11
%e A223322 11 -> 3 5 7 9 10
%Y A223322 Cf. A223321.
%K A223322 nonn
%O A223322 1,1
%A A223322 _R. H. Hardin_, Mar 19 2013