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 A223321 T(n,k)=Rolling icosahedron footprints: number of nXk 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge 9
 1, 5, 12, 25, 125, 144, 125, 1625, 3125, 1728, 625, 21125, 105625, 78125, 20736, 3125, 274625, 3570125, 6865625, 1953125, 248832, 15625, 3570125, 122039125, 603351125, 446265625, 48828125, 2985984, 78125, 46411625, 4176940625, 54279694625 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts ........1...........5..............25................125....................625 .......12.........125............1625..............21125.................274625 ......144........3125..........105625............3570125..............122039125 .....1728.......78125.........6865625..........603351125............54279694625 ....20736.....1953125.......446265625.......101966340125.........24143758634125 ...248832....48828125.....29007265625.....17232311481125......10739266230499625 ..2985984..1220703125...1885472265625...2912260640310125....4776881955584279125 .35831808.30517578125.122555697265625.492172048212411125.2124782217358970404625 LINKS R. H. Hardin, Table of n, a(n) for n = 1..97 FORMULA Empirical for column k: k=1: a(n) = 12*a(n-1) k=2: a(n) = 25*a(n-1) k=3: a(n) = 65*a(n-1) k=4: a(n) = 169*a(n-1) k=5: a(n) = 479*a(n-1) -15210*a(n-2) k=6: a(n) = 1366*a(n-1) -232713*a(n-2) +9253764*a(n-3) k=7: [order 8] Empirical for row n: n=1: a(n) = 5*a(n-1) n=2: a(n) = 13*a(n-1) for n>2 n=3: a(n) = 38*a(n-1) -129*a(n-2) for n>4 n=4: [order 7] for n>10 n=5: [order 32] for n>36 EXAMPLE Some solutions for n=3 k=4 ..0..1..8..9....0..1..0..7....0..1..0..2....0..1..0..6....0..6..2..4 ..0..2..8..2....0..5..0..5....0..6..0..2....0..6.10..5....0..1..2..4 ..6..2..4..2....0..1..0..7....0..7..0..7....0..6.10..5....0..6.10..4 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 Column 1 is A001021(n-1) Column 2 is A013710(n-1) Column 3 is 25*65^(n-1) Column 4 is 125*169^(n-1) Row 1 is A000351(n-1) Sequence in context: A289586 A223233 A038254 * A073095 A309323 A294017 Adjacent sequences:  A223318 A223319 A223320 * A223322 A223323 A223324 KEYWORD nonn,tabl AUTHOR R. H. Hardin Mar 19 2013 STATUS approved

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Last modified July 23 22:20 EDT 2021. Contains 346265 sequences. (Running on oeis4.)