A223234 - OEIS

%I #7 Aug 17 2018 09:22:44

%S 12,65,785,7445,75665,753005,7540985,75377045,753868865,7538393405,

%T 75384819785,753845540645,7538463378065,75384609865805,

%U 753846170402585,7538461488792245,75384615533623265,753846153399130205

%N Rolling icosahedron footprints: number of 2 X n 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an icosahedral edge.

%C Row 2 of A223233.

%H R. H. Hardin, <a href="/A223234/b223234.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) + 30*a(n-2) for n>3.

%F Conjectures from _Colin Barker_, Aug 17 2018: (Start)

%F G.f.: x*(12 - 19*x - 30*x^2) / ((1 + 3*x)*(1 - 10*x)).

%F a(n) = (-25*(-1)^n*3^(1+n) + 49*10^n) / 65 for n>1.

%F (End)

%e Some solutions for n=3:

%e ..0..2..1....0..7.11....0..6..2....0..6..5....0..7..3....0..2..1....0..2..0

%e ..0..7..0....3..7..3...10..6..4....4..6..5....3..7..0....6..2..8....8..2..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. A223233.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 18 2013