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 A223209 T(n,k)=Rolling icosahedron face footprints: number of nXk 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or vertical neighbor moves across an icosahedral edge 7
 1, 3, 3, 9, 15, 9, 27, 75, 75, 27, 81, 375, 657, 375, 81, 243, 1875, 5763, 5763, 1875, 243, 729, 9375, 50553, 90111, 50553, 9375, 729, 2187, 46875, 443451, 1412907, 1412907, 443451, 46875, 2187, 6561, 234375, 3889953, 22163655, 39868737, 22163655 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts ......1.........3............9..............27.................81 ......3........15...........75.............375...............1875 ......9........75..........657............5763..............50553 .....27.......375.........5763...........90111............1412907 .....81......1875........50553.........1412907...........39868737 ....243......9375.......443451........22163655.........1127761923 ....729.....46875......3889953.......347696019........31921015497 ...2187....234375.....34122675......5454600015.......903661481115 ...6561...1171875....299324169.....85571052219.....25583075832465 ..19683...5859375...2625672171...1342427863959....724276345970163 ..59049..29296875..23032401201..21059839795875..20504869741550745 .177147.146484375.202040266467.330384125138847.580510427181846027 LINKS R. H. Hardin, Table of n, a(n) for n = 1..220 FORMULA Empirical for column k: k=1: a(n) = 3*a(n-1) k=2: a(n) = 5*a(n-1) k=3: a(n) = 9*a(n-1) -2*a(n-2) k=4: a(n) = 19*a(n-1) -54*a(n-2) +32*a(n-3) k=5: a(n) = 31*a(n-1) -24*a(n-2) -1612*a(n-3) +3816*a(n-4) +1152*a(n-5) -2784*a(n-6) +256*a(n-7) k=6: [order 12] k=7: [order 28] EXAMPLE Some solutions for n=3 k=4 ..0..2..0..1....0..2..0..2....0..5..0..2....0..2..3..4....0..1..6.10 ..2..8..2..0....2..8..2..8....5..9..5..0....2..0..2..3....1..6..1..6 ..3..2..3..2....3..2..8.13....0..5..0..5....0..2..8..2....4..1..4..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 CROSSREFS Column 1 is A000244(n-1) Column 2 is A005053 Sequence in context: A122847 A197462 A264098 * A233026 A105423 A147471 Adjacent sequences:  A223206 A223207 A223208 * A223210 A223211 A223212 KEYWORD nonn,tabl AUTHOR R. H. Hardin Mar 18 2013 STATUS approved

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Last modified May 27 13:04 EDT 2022. Contains 354097 sequences. (Running on oeis4.)