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A180360
Table t(n,k) is the number of ways to partition 1 into k fractions using the Farey fractions of order n, read row by row.
3
1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 5, 4, 2, 1, 1, 6, 6, 5, 3, 1, 1, 9, 10, 8, 5, 2, 1, 1, 11, 14, 13, 10, 6, 3, 1, 1, 14, 20, 22, 21, 15, 9, 4, 1, 1, 16, 26, 36, 39, 33, 22, 11, 4, 1, 1, 21, 36, 47, 49, 40, 27, 14, 6, 2, 1, 1, 23, 44, 70, 87, 89, 76, 53, 31, 14, 5, 1, 1, 29, 58, 88, 105, 103, 87
OFFSET
1,5
COMMENTS
...
..1
..1...1
..1...2...1
..1...3...2...1
..1...5...4...2...1
..1...6...6...5...3...1
..1...9..10...8...5...2...1
..1..11..14..13..10...6...3...1
..1..14..20..22..21..15...9...4...1
..1..16..26..36..39..33..22..11...4...1
..1..21..36..47..49..40..27..14...6...2...1
..1..23..44..70..87..89..76..53..31..14...5...1
..1..29..58..88.105.103..87..60..36..17...7...2...1
...
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..389.
EXAMPLE
t(6,3) = 6 because 1 = 2/3+1/6+1/6 = 3/5+1/5+1/5 = 1/2+1/3+1/6 = 1/2+1/4+1/4 = 2/5+2/5+1/5 = 1/3+1/3+1/3.
MATHEMATICA
Farey[n_] := Union@ Flatten@ Table[a/b, {b, n}, {a, b}]; t[n_, k_] := Length@ IntegerPartitions[1, {k}, Farey@ n]; Table[ t[n, k], {n, 13}, {k, n}] // Flatten
CROSSREFS
Row sum A119983, first column and main diagonal A000012, second column A046657.
Sequence in context: A027293 A104762 A152462 * A318805 A175331 A098805
KEYWORD
nonn,tabl
AUTHOR
Robert G. Wilson v, Aug 30 2010
STATUS
approved