cp's OEIS Frontend

A223482 Rolling icosahedron face footprints: number of 4 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 A223482 #7 Aug 20 2018 14:38:35
%S A223482 8000,2187,30375,421875,6526575,101331675,1588785975,24919035075,
%T A223482 390919514175,6132664672875,96208422848775,1509305488830675,
%U A223482 23677794878309775,371454275512532475,5827328087571285975
%N A223482 Rolling icosahedron face footprints: number of 4 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 A223482 Row 4 of A223480.
%H A223482 R. H. Hardin, <a href="/A223482/b223482.txt">Table of n, a(n) for n = 1..210</a>
%F A223482 Empirical: a(n) = 17*a(n-1) - 16*a(n-2) - 76*a(n-3) + 64*a(n-4) for n>7.
%F A223482 Empirical g.f.: x*(8000 - 133813*x + 121196*x^2 + 548492*x^3 - 505088*x^4 - 701568*x^5 + 691200*x^6) / ((1 + 2*x)*(1 - 19*x + 54*x^2 - 32*x^3)). - _Colin Barker_, Aug 20 2018
%e A223482 Some solutions for n=3:
%e A223482 ..0..2..3....0..5..9....0..2..8....0..5..9....0..1..6....0..2..3....0..1..4
%e A223482 ..0..2..8....7..5..7....3..2..8....9..5..7....6.10..6....8..2..0....0..1..6
%e A223482 ..8..2..0....7..6..1....0..2..8....7..6..7....6..7..6....0..1..6....6..7.11
%e A223482 ..8..2..8....7..6..7....8..2..8....7..5..9....6.10.12....6..1..0....6..7..6
%e A223482 Face neighbors:
%e A223482 0 -> 1 2 5
%e A223482 1 -> 0 4 6
%e A223482 2 -> 0 3 8
%e A223482 3 -> 2 4 16
%e A223482 4 -> 3 1 17
%e A223482 5 -> 0 7 9
%e A223482 6 -> 1 7 10
%e A223482 7 -> 6 5 11
%e A223482 8 -> 2 9 13
%e A223482 9 -> 8 5 14
%e A223482 10 -> 6 12 17
%e A223482 11 -> 7 12 14
%e A223482 12 -> 11 10 19
%e A223482 13 -> 8 15 16
%e A223482 14 -> 9 11 15
%e A223482 15 -> 14 13 19
%e A223482 16 -> 3 13 18
%e A223482 17 -> 4 10 18
%e A223482 18 -> 16 17 19
%e A223482 19 -> 15 18 12
%Y A223482 Cf. A223480.
%K A223482 nonn
%O A223482 1,1
%A A223482 _R. H. Hardin_, Mar 20 2013