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 A223282 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, diagonal or antidiagonal neighbor moves across an icosahedral edge 13
 1, 3, 20, 9, 15, 400, 27, 87, 75, 8000, 81, 351, 849, 375, 160000, 243, 1575, 4995, 8295, 1875, 3200000, 729, 6831, 38457, 72279, 81057, 9375, 64000000, 2187, 29943, 261819, 1024071, 1048923, 792087, 46875, 1280000000, 6561, 130815, 1881441, 10979127 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts ............1.......3..........9...........27..............81...............243 ...........20......15.........87..........351............1575..............6831 ..........400......75........849.........4995...........38457............261819 .........8000.....375.......8295........72279.........1024071..........10979127 .......160000....1875......81057......1048923........28271577.........473368227 ......3200000....9375.....792087.....15229647.......792881031.......20570223999 .....64000000...46875....7740273....221142771.....22392745881......895927195659 ...1280000000..234375...75637959...3211159815....634400697159....39047604482055 ..25600000000.1171875..739134273..46628577099..17998034165721..1702160040384051 .512000000000.5859375.7222821495.677084057343.510923724667143.74204651599582287 LINKS R. H. Hardin, Table of n, a(n) for n = 1..161 FORMULA Empirical for column k: k=1: a(n) = 20*a(n-1) k=2: a(n) = 5*a(n-1) k=3: a(n) = 11*a(n-1) -12*a(n-2) k=4: a(n) = 17*a(n-1) -36*a(n-2) k=5: a(n) = 45*a(n-1) -518*a(n-2) +1268*a(n-3) +1704*a(n-4) -4064*a(n-5) +1536*a(n-6) k=6: [order 9] k=7: [order 20] Empirical for row n: n=1: a(n) = 3*a(n-1) n=2: a(n) = 3*a(n-1) +6*a(n-2) for n>3 n=3: a(n) = 5*a(n-1) +18*a(n-2) -24*a(n-3) for n>4 n=4: 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 n=5: [order 12] for n>13 n=6: [order 26] for n>27 EXAMPLE Some solutions for n=3 k=4 ..0..5..0..5....0..5..0..5....0..5..0..5....0..2..0..2....0..5..7..5 ..0..2..0..5....0..2..0..5....0..5..0..1....0..2..0..2....7..5..0..5 ..8..2..0..2....3..2..0..1....0..2..0..2....0..5..0..2....9..5..0..2 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 A009964(n-1) Column 2 is A005053 Row 1 is A000244(n-1) Sequence in context: A260371 A067607 A013332 * A223480 A063871 A084316 Adjacent sequences:  A223279 A223280 A223281 * A223283 A223284 A223285 KEYWORD nonn,tabl AUTHOR R. H. Hardin Mar 19 2013 STATUS approved

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Last modified August 11 12:12 EDT 2022. Contains 356065 sequences. (Running on oeis4.)