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.

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

Adjacent sequences: A180357 A180358 A180359 * A180361 A180362 A180363

Keyword

nonn,tabl

Author

Robert G. Wilson v, Aug 30 2010

Status

approved