A223279 Rolling icosahedron face footprints: number of n X 5 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.
81, 1575, 38457, 1024071, 28271577, 792881031, 22392745881, 634400697159, 17998034165721, 510923724667143, 14507984391789081, 412013548109024967, 11701449873880124505, 332336795068373382279, 9438910778776181239449
Offset: 1
Keywords
Examples
Some solutions for n=3: 0 1 0 1 4 0 1 0 5 9 0 5 0 2 0 0 1 4 1 6 6 1 0 1 0 0 5 0 5 7 0 5 0 2 8 4 1 4 1 4 0 1 0 1 6 9 5 0 5 9 9 5 0 2 3 6 1 6 1 6 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) = 45*a(n-1) - 518*a(n-2) + 1268*a(n-3) + 1704*a(n-4) - 4064*a(n-5) + 1536*a(n-6).
Empirical g.f.: 3*x*(9 - 68*x + 64*x^2)*(3 - 54*x - 76*x^2 + 56*x^3) / (1 - 45*x + 518*x^2 - 1268*x^3 - 1704*x^4 + 4064*x^5 - 1536*x^6). - Colin Barker, Aug 18 2018
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