cp's OEIS Frontend

A223323 Rolling icosahedron footprints: number of 3 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 A223323 #8 Aug 19 2018 09:36:41
%S A223323 144,3125,105625,3570125,122039125,4176940625,142980696625,
%T A223323 4894441131125,167544253118125,5735298712573625,196328142425559625,
%U A223323 6720615878249268125,230057073000574997125,7875209325727694302625,269580591960578208870625
%N A223323 Rolling icosahedron footprints: number of 3 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 A223323 Row 3 of A223321.
%H A223323 R. H. Hardin, <a href="/A223323/b223323.txt">Table of n, a(n) for n = 1..210</a>
%F A223323 Empirical: a(n) = 38*a(n-1) - 129*a(n-2) for n>4.
%F A223323 Empirical g.f.: x*(144 - 2347*x + 5451*x^2 - 40500*x^3) / (1 - 38*x + 129*x^2). - _Colin Barker_, Aug 19 2018
%e A223323 Some solutions for n=3:
%e A223323 ..0..6..5....0..7..3....0..1..8....0..7.11....0..7.11....0..7..1....0..7..1
%e A223323 ..4.10..4....3..8..2....0..1..8....3..7..3....0..7..1....1..2..8....1..8..4
%e A223323 .11..9..3....1..8..1....2..1..2....3..9..8...11..3..7....0..1..7....9..8..4
%e A223323 Vertex neighbors:
%e A223323 0 -> 1 2 5 6 7
%e A223323 1 -> 0 2 3 7 8
%e A223323 2 -> 0 1 4 6 8
%e A223323 3 -> 1 7 8 9 11
%e A223323 4 -> 2 6 8 9 10
%e A223323 5 -> 0 6 7 10 11
%e A223323 6 -> 0 2 4 5 10
%e A223323 7 -> 0 1 3 5 11
%e A223323 8 -> 1 2 3 4 9
%e A223323 9 -> 3 4 8 10 11
%e A223323 10 -> 4 5 6 9 11
%e A223323 11 -> 3 5 7 9 10
%Y A223323 Cf. A223321.
%K A223323 nonn
%O A223323 1,1
%A A223323 _R. H. Hardin_, Mar 19 2013