A223285 Rolling icosahedron face footprints: number of 4 X n 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.
8000, 375, 8295, 72279, 1024071, 10979127, 137621799, 1576368663, 19009505799, 222545715447, 2650002132711, 31248496329687, 370552575553479, 4379948164268727, 51867287743753383, 613557282050858391
Offset: 1
Keywords
Examples
Some solutions for n=3: 0 1 0 0 2 0 0 2 8 0 5 7 0 1 4 0 2 3 0 1 4 4 1 4 0 2 8 8 2 3 9 5 9 4 1 0 8 2 0 6 1 6 6 1 4 0 2 3 0 2 8 9 5 0 0 1 6 0 2 8 6 1 6 6 1 0 8 2 8 3 2 0 9 5 0 6 1 6 0 2 8 4 1 0 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) = 5*a(n-1) + 92*a(n-2) - 56*a(n-3) - 920*a(n-4) + 192*a(n-5) + 1152*a(n-6) for n>7.
Empirical g.f.: x*(8000 - 39625*x - 729580*x^2 + 444304*x^3 + 7280536*x^4 - 1517376*x^5 - 9097344*x^6) / (1 - 5*x - 92*x^2 + 56*x^3 + 920*x^4 - 192*x^5 - 1152*x^6). - Colin Barker, Aug 18 2018
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