A223323 - OEIS

%I #8 Aug 19 2018 09:36:41

%S 144,3125,105625,3570125,122039125,4176940625,142980696625,

%T 4894441131125,167544253118125,5735298712573625,196328142425559625,

%U 6720615878249268125,230057073000574997125,7875209325727694302625,269580591960578208870625

%N 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 Row 3 of A223321.

%H R. H. Hardin, <a href="/A223323/b223323.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 38*a(n-1) - 129*a(n-2) for n>4.

%F 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 Some solutions for n=3:

%e ..0..6..5....0..7..3....0..1..8....0..7.11....0..7.11....0..7..1....0..7..1

%e ..4.10..4....3..8..2....0..1..8....3..7..3....0..7..1....1..2..8....1..8..4

%e .11..9..3....1..8..1....2..1..2....3..9..8...11..3..7....0..1..7....9..8..4

%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