cp's OEIS Frontend

A223481 Rolling icosahedron face footprints: number of 3 X n 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 A223481 #8 Aug 20 2018 14:38:27
%S A223481 400,243,2025,16875,147825,1296675,11374425,99776475,875239425,
%T A223481 7677601875,67347938025,590776238475,5182290270225,45459059955075,
%U A223481 398766959055225,3497984511586875,30684326686171425,269162971152369075
%N A223481 Rolling icosahedron face footprints: number of 3 X n 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 A223481 Row 3 of A223480.
%H A223481 R. H. Hardin, <a href="/A223481/b223481.txt">Table of n, a(n) for n = 1..210</a>
%F A223481 Empirical: a(n) = 9*a(n-1) - 2*a(n-2) for n>4.
%F A223481 Empirical g.f.: x*(400 - 3357*x + 638*x^2 - 864*x^3) / (1 - 9*x + 2*x^2). - _Colin Barker_, Aug 20 2018
%e A223481 Some solutions for n=3:
%e A223481 ..0..2..3....0..1..0....0..2..8....0..5..0....0..1..0....0..2..0....0..1..6
%e A223481 ..3..4..1....0..2..8....3..2..8....0..5..9....0..2..0....3..2..3....6..1..6
%e A223481 ..1..4..1....8..2..8....8..9..5....9..8..2....3..2..8....3..4..1....6.10.12
%e A223481 Face neighbors:
%e A223481 0 -> 1 2 5
%e A223481 1 -> 0 4 6
%e A223481 2 -> 0 3 8
%e A223481 3 -> 2 4 16
%e A223481 4 -> 3 1 17
%e A223481 5 -> 0 7 9
%e A223481 6 -> 1 7 10
%e A223481 7 -> 6 5 11
%e A223481 8 -> 2 9 13
%e A223481 9 -> 8 5 14
%e A223481 10 -> 6 12 17
%e A223481 11 -> 7 12 14
%e A223481 12 -> 11 10 19
%e A223481 13 -> 8 15 16
%e A223481 14 -> 9 11 15
%e A223481 15 -> 14 13 19
%e A223481 16 -> 3 13 18
%e A223481 17 -> 4 10 18
%e A223481 18 -> 16 17 19
%e A223481 19 -> 15 18 12
%Y A223481 Cf. A223480.
%K A223481 nonn
%O A223481 1,1
%A A223481 _R. H. Hardin_, Mar 20 2013