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%I A180360 #11 Jan 31 2017 11:02:27
%S A180360 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,
%T A180360 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,
%U A180360 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
%N 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.
%C A180360 ...
%C A180360 ..1
%C A180360 ..1...1
%C A180360 ..1...2...1
%C A180360 ..1...3...2...1
%C A180360 ..1...5...4...2...1
%C A180360 ..1...6...6...5...3...1
%C A180360 ..1...9..10...8...5...2...1
%C A180360 ..1..11..14..13..10...6...3...1
%C A180360 ..1..14..20..22..21..15...9...4...1
%C A180360 ..1..16..26..36..39..33..22..11...4...1
%C A180360 ..1..21..36..47..49..40..27..14...6...2...1
%C A180360 ..1..23..44..70..87..89..76..53..31..14...5...1
%C A180360 ..1..29..58..88.105.103..87..60..36..17...7...2...1
%C A180360 ...
%H A180360 Robert G. Wilson v, <a href="/A180360/b180360.txt">Table of n, a(n) for n = 1..389</a>.
%e A180360 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.
%t A180360 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
%Y A180360 Row sum A119983, first column and main diagonal A000012, second column A046657.
%K A180360 nonn,tabl
%O A180360 1,5
%A A180360 _Robert G. Wilson v_, Aug 30 2010

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