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 A223181 Rolling icosahedron footprints: number of n X 3 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, vertical or antidiagonal neighbor moves along an icosahedral edge. 1
 25, 80, 400, 2080, 10880, 56960, 298240, 1561600, 8176640, 42813440, 224174080, 1173790720, 6146048000, 32181125120, 168502558720, 882290851840, 4619734876160, 24189245849600, 126656535592960, 663182230159360 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Column 3 of A223186. LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 FORMULA Empirical: a(n) = 6*a(n-1) - 4*a(n-2) for n>3. Conjectures from Colin Barker, Aug 17 2018: (Start) G.f.: 5*x*(5 - 14*x + 4*x^2) / (1 - 6*x + 4*x^2). a(n) = sqrt(5)*((3-sqrt(5))^n*(1+sqrt(5)) + (-1+sqrt(5))*(3+sqrt(5))^n) for n>1. (End) EXAMPLE Some solutions for n=3: ..0..7..1....0..2..6....0..5..7....0..2..6....0..5.10....0..6..4....0..7..1 ..5..0..2....6..0..2....7.11..5....6..4..2....7.11..5....5.10..6....1..0..2 ..7..1..0....2..1..0....5..7.11....2..6..4....5.10..6....6..5..0....2..1..8 Vertex neighbors: 0 -> 1 2 5 6 7 1 -> 0 2 3 7 8 2 -> 0 1 4 6 8 3 -> 1 7 8 9 11 4 -> 2 6 8 9 10 5 -> 0 6 7 10 11 6 -> 0 2 4 5 10 7 -> 0 1 3 5 11 8 -> 1 2 3 4 9 9 -> 3 4 8 10 11 10 -> 4 5 6 9 11 11 -> 3 5 7 9 10 CROSSREFS Cf. A223186. Sequence in context: A080699 A134153 A251311 * A016814 A280343 A204708 Adjacent sequences:  A223178 A223179 A223180 * A223182 A223183 A223184 KEYWORD nonn AUTHOR R. H. Hardin, Mar 18 2013 STATUS approved

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Last modified September 23 05:28 EDT 2021. Contains 347609 sequences. (Running on oeis4.)