A223278 Rolling icosahedron face footprints: number of n X 4 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.
27, 351, 4995, 72279, 1048923, 15229647, 221142771, 3211159815, 46628577099, 677084057343, 9831800199267, 142765577323191, 2073070007320635, 30102629340815919, 437114178530327763, 6347246378746198887
Offset: 1
Keywords
Examples
Some solutions for n=3: ..0..2..3.16....0..2..0..1....0..1..0..1....0..2..0..1....0..5..0..1 ..8..2..3..2....0..5..0..1....4..1..4..1....0..1..0..5....0..2..0..1 ..3..2..3.16....7..5..0..5....4..1..6..1....4..1..0..5....3..2..0..5 Face neighbors: 0 -> 1 2 5 1 -> 0 4 6 2 -> 0 3 8 3 -> 2 4 16 4 -> 3 1 17 5 -> 0 7 9 6 -> 1 7 10 7 -> 6 5 11 8 -> 2 9 13 9 -> 8 5 14 10 -> 6 12 17 11 -> 7 12 14 12 -> 11 10 19 13 -> 8 15 16 14 -> 9 11 15 15 -> 14 13 19 16 -> 3 13 18 17 -> 4 10 18 18 -> 16 17 19 19 -> 15 18 12
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A223282.
Formula
Empirical: a(n) = 17*a(n-1) - 36*a(n-2).
Conjectures from Colin Barker, Aug 18 2018: (Start)
G.f.: 27*x*(1 - 4*x) / (1 - 17*x + 36*x^2).
a(n) = (3*2^(-1-n)*((17-sqrt(145))^n*(-1+sqrt(145)) + (1+sqrt(145))*(17+sqrt(145))^n)) / sqrt(145).
(End)
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