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

Author

Robert G. Wilson v, Aug 30 2010

Keywords

• nonn
• tabl

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

...

Examples

			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.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..389.

Crossrefs

Row sum A119983, first column and main diagonal A000012, second column A046657.

Programs

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