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 A223235 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, diagonal or antidiagonal neighbor moves along an icosahedral edge. 1

%I #7 Aug 17 2018 09:23:04

%S 144,845,25225,492365,11043445,236027705,5127809545,110781320885,

%T 2397904326205,51869658014705,1122255717889585,24279356422739885,

%U 525283571663978725,11364402460546714985,245867265513538637785

%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, diagonal or antidiagonal neighbor moves along an icosahedral edge.

%C Row 3 of A223233.

%H R. H. Hardin, <a href="/A223235/b223235.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 18*a(n-1) + 103*a(n-2) - 552*a(n-3) + 540*a(n-4) for n>5.

%F Empirical g.f.: x*(144 - 1747*x - 4817*x^2 + 30768*x^3 - 28620*x^4) / (1 - 18*x - 103*x^2 + 552*x^3 - 540*x^4). - _Colin Barker_, Aug 17 2018

%e Some solutions for n=3:

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

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

%e .11..5..0....0..5..6....5..7..0....4..2..1....4..2..0....3..7..0....7..1..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. A223233.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 18 2013

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Last modified August 12 15:11 EDT 2024. Contains 375113 sequences. (Running on oeis4.)