cp's OEIS Frontend

A223205 Rolling icosahedron face footprints: number of n X 4 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or vertical neighbor moves across an icosahedral edge.

%I A223205 #8 Aug 17 2018 09:22:14
%S A223205 27,375,5763,90111,1412907,22163655,347696019,5454600015,85571052219,
%T A223205 1342427863959,21059839795875,330384125138847,5183024720307531,
%U A223205 81310641801813351,1275591151342290099,20011314009255431919
%N A223205 Rolling icosahedron face footprints: number of n X 4 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or vertical neighbor moves across an icosahedral edge.
%C A223205 Column 4 of A223209.
%H A223205 R. H. Hardin, <a href="/A223205/b223205.txt">Table of n, a(n) for n = 1..210</a>
%F A223205 Empirical: a(n) = 19*a(n-1) - 54*a(n-2) + 32*a(n-3).
%F A223205 Empirical g.f.: 3*x*(9 - 46*x + 32*x^2) / (1 - 19*x + 54*x^2 - 32*x^3). - _Colin Barker_, Aug 17 2018
%e A223205 Some solutions for n=3:
%e A223205 ..0..1..6.10....0..2..3..2....0..5..9..8....0..1..0..2....0..1..4.17
%e A223205 ..1..0..1..6....2..3..2..3....5..9.14..9....1..6..1..0....1..0..1..4
%e A223205 ..4..1..6.10....3..2..3.16....9.14..9..5....0..1..0..2....4..1..6..1
%e A223205 Face neighbors:
%e A223205 0 -> 1 2 5
%e A223205 1 -> 0 4 6
%e A223205 2 -> 0 3 8
%e A223205 3 -> 2 4 16
%e A223205 4 -> 3 1 17
%e A223205 5 -> 0 7 9
%e A223205 6 -> 1 7 10
%e A223205 7 -> 6 5 11
%e A223205 8 -> 2 9 13
%e A223205 9 -> 8 5 14
%e A223205 10 -> 6 12 17
%e A223205 11 -> 7 12 14
%e A223205 12 -> 11 10 19
%e A223205 13 -> 8 15 16
%e A223205 14 -> 9 11 15
%e A223205 15 -> 14 13 19
%e A223205 16 -> 3 13 18
%e A223205 17 -> 4 10 18
%e A223205 18 -> 16 17 19
%e A223205 19 -> 15 18 12
%Y A223205 Cf. A223209.
%K A223205 nonn
%O A223205 1,1
%A A223205 _R. H. Hardin_, Mar 18 2013