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 A223480 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 antidiagonal neighbor moves across an icosahedral edge 10
 1, 3, 20, 9, 27, 400, 27, 135, 243, 8000, 81, 675, 2025, 2187, 160000, 243, 3375, 16875, 30375, 19683, 3200000, 729, 16875, 147825, 421875, 455625, 177147, 64000000, 2187, 84375, 1296675, 6526575, 10546875, 6834375, 1594323, 1280000000, 6561, 421875 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts ..........1........3..........9...........27.............81..............243 .........20.......27........135..........675...........3375............16875 ........400......243.......2025........16875.........147825..........1296675 .......8000.....2187......30375.......421875........6526575........101331675 .....160000....19683.....455625.....10546875......288507825.......7939566675 ....3200000...177147....6834375....263671875....12755926575.....622332801675 ...64000000..1594323..102515625...6591796875...563999907825...48783753036675 .1280000000.14348907.1537734375.164794921875.24937217326575.3824122400271675 LINKS R. H. Hardin, Table of n, a(n) for n = 1..160 FORMULA Empirical for column k: k=1: a(n) = 20*a(n-1) k=2: a(n) = 9*a(n-1) k=3: a(n) = 15*a(n-1) k=4: a(n) = 25*a(n-1) k=5: a(n) = 51*a(n-1) -300*a(n-2) k=6: a(n) = 101*a(n-1) -1900*a(n-2) +10000*a(n-3) k=7: a(n) = 227*a(n-1) -14764*a(n-2) +411840*a(n-3) -5347200*a(n-4) +29600000*a(n-5) -48000000*a(n-6) Empirical for row n: n=1: a(n) = 3*a(n-1) n=2: a(n) = 5*a(n-1) for n>2 n=3: a(n) = 9*a(n-1) -2*a(n-2) for n>4 n=4: a(n) = 17*a(n-1) -16*a(n-2) -76*a(n-3) +64*a(n-4) for n>7 n=5: 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 n=6: [order 20] for n>25 EXAMPLE Some solutions for n=3 k=4 ..0..1..6.10....0..1..4..1....0..1..0..1....0..2..8.13....0..2..8..9 ..6..1..6..1....6..1..4..3....4..1..0..5....0..2..8..2....8..9..8..9 ..4..1..4..3....4.17..4.17....0..5..9..5....8..2..3..4....8..2..8..9 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 A013708(n-1) Column 3 is 9*15^(n-1) Column 4 is 27*25^(n-1) Row 1 is A000244(n-1) Row 2 is 27*5^(n-2) for n>1 Sequence in context: A067607 A013332 A223282 * A063871 A084316 A126810 Adjacent sequences: A223477 A223478 A223479 * A223481 A223482 A223483 KEYWORD nonn,tabl AUTHOR R. H. Hardin Mar 20 2013 STATUS approved

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Last modified December 5 09:29 EST 2023. Contains 367589 sequences. (Running on oeis4.)