A223483 Rolling icosahedron face footprints: number of 5Xn 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves across an icosahedral edge.
160000, 19683, 455625, 10546875, 288507825, 7939566675, 223894186425, 6318290752875, 178826926010625, 5061686863486275, 143298073856716425, 4056837300096090075, 114852424247153593425, 3251568434305627847475
Offset: 1
Keywords
Examples
Some solutions for n=3 ..0..5..0....0..5..0....0..5..0....0..5..0....0..5..7....0..5..0....0..5..7 ..7..5..7....0..1..4....9..5..0....0..2..0....0..5..7....0..5..0....7..6..7 ..9..5..9....4.17..4....0..2..8....0..2..8....7..5..9....0..5..7....7..5..9 ..9..8.13....4.17..4....3..2..8....8..2..3....7..5..0....7..6..1....7..5..7 ..2..8..2...18.17..4....8.13..8....0..2..3....0..1..0....1..0..2....7..6..1 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
Formula
Empirical: a(n) = 33*a(n-1) -86*a(n-2) -1564*a(n-3) +7040*a(n-4) -6480*a(n-5) -5088*a(n-6) +5824*a(n-7) -512*a(n-8) for n>13
Comments