A223322 - OEIS

%I #9 Jun 29 2023 11:16:29

%S 12,125,1625,21125,274625,3570125,46411625,603351125,7843564625,

%T 101966340125,1325562421625,17232311481125,224020049254625,

%U 2912260640310125,37859388324031625,492172048212411125

%N 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 Row 2 of A223321.

%H R. H. Hardin, <a href="/A223322/b223322.txt">Table of n, a(n) for n = 1..210</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (13).

%F Empirical: a(n) = 13*a(n-1) for n>2.

%F Conjectures from _Colin Barker_, Aug 19 2018: (Start)

%F G.f.: x*(12 - 31*x) / (1 - 13*x).

%F a(n) = 125*13^(n-2) for n>1.

%F (End)

%e Some solutions for n=3:

%e ..0..7..3....0..2..8....0..2..4....0..5.11....0..6..5....0..1..3....0..7..0

%e ..1..8..4....8..1..2....8..2..1...10..9..4....2..6..2....3.11..3....0..1..7

%e Vertex neighbors:

%e 0 -> 1 2 5 6 7

%e 1 -> 0 2 3 7 8

%e 2 -> 0 1 4 6 8

%e 3 -> 1 7 8 9 11

%e 4 -> 2 6 8 9 10

%e 5 -> 0 6 7 10 11

%e 6 -> 0 2 4 5 10

%e 7 -> 0 1 3 5 11

%e 8 -> 1 2 3 4 9

%e 9 -> 3 4 8 10 11

%e 10 -> 4 5 6 9 11

%e 11 -> 3 5 7 9 10

%Y Cf. A223321.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 19 2013