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 A223258 Rolling icosahedron footprints: number of n X 3 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or vertical neighbor moves along an icosahedral edge. 1

%I

%S 25,845,28885,988625,33841585,1158447605,39655444525,1357467150905,

%T 46468199390665,1590678314378525,54451378224988165,

%U 1863954869994720545,63806057268775907425,2184179997984165531845,74767858535726198152285

%N Rolling icosahedron footprints: number of n X 3 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or vertical neighbor moves along an icosahedral edge.

%C Column 3 of A223263.

%H R. H. Hardin, <a href="/A223258/b223258.txt">Table of n, a(n) for n = 1..210</a>

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

%F Conjectures from _Colin Barker_, Aug 18 2018: (Start)

%F G.f.: 5*x*(5 - 21*x) / (1 - 38*x + 129*x^2).

%F a(n) = (5*((19-2*sqrt(58))^n*(-41+7*sqrt(58)) + (19+2*sqrt(58))^n*(41+7*sqrt(58)))) / (86*sqrt(58)).

%F (End)

%e Some solutions for n=3:

%e ..0..1..3....0..6..2....0..5..6....0..1..8....0..7..1....0..7..1....0..2..8

%e ..6..2..8....5.10..6....5.10..5....1..0..2....6..5..0....7..1..3....1..8..4

%e ..2..0..2...10..6..2....7..5..7....7..5..0....2..0..1....5..7.11....8..4..8

%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. A223263.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 19 2013

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Last modified January 27 12:02 EST 2022. Contains 350607 sequences. (Running on oeis4.)