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 A226646 Number of ways to express m/n as Egyptian fractions in just three terms, that is, m/n = 1/x + 1/y + 1/z satisfying 1 <= x <= y <= z and read by antidiagonals. 6
 3, 1, 10, 1, 3, 21, 0, 3, 8, 28, 0, 1, 3, 10, 36, 0, 1, 3, 6, 12, 57, 0, 1, 2, 3, 10, 21, 42, 0, 0, 1, 4, 2, 10, 17, 70, 0, 0, 1, 3, 3, 8, 9, 28, 79, 0, 0, 0, 1, 3, 4, 7, 20, 26, 96, 0, 0, 1, 1, 2, 3, 4, 10, 21, 36, 62, 0, 0, 0, 1, 1, 7, 1, 7, 6, 21, 25, 160, 0, 0, 0, 1, 0, 3, 3, 6, 12, 12, 16, 57, 59 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A073101 for the 4/n conjecture due to Erdös and Straus. The first upper diagonal is 10, 8, 6, 2, 4, 1, 2, 1, 2, 0, 3, 0, 0, 1, 0, 0, 1, 0, 1, 0,... . The main diagonal is: 3, 3, 3, 3, 3, 3, ... since 1 = 1/2 + 1/3 + 1/6 = 1/2 + 1/4 + 1/4 = 1/3 + 1/3 + 1/3. See A002966(3). The first lower diagonal is 1, 3, 3, 4, 3, 7, 3, 5, 4, 6, 3, 10, 3, 6, 6, 6, 3, 9, 3, 9, ... . The antidiagonal sum is 3, 11, 25, 39, 50, 79, 79, 104, 131, 157, 140, 229, 169, 220, 295, 282, ... . LINKS Christian Elsholtz, Sums Of k Unit Fractions David Eppstein, Algorithms for Egyptian Fractions David Eppstein, Ten Algorithms for Egyptian Fractions Ron Knott Egyptian Fractions Oakland University The Erdős Number Project Eric Weisstein's World of Mathematics, Egyptian Fraction EXAMPLE ../n m/ 1...2...3...4...5...6...7...8...9..10..11...12..13...14...15 =Allocation nbr. .1 3..10..21..28..36..57..42..70..79..96..62..160..59..136..196 A004194 .2 1...3...8..10..12..21..17..28..26..36..25...57..20...42...81 A226641 .3 1...3...3...6..10..10...9..20..21..21..16...28..11...33...36 A226642 .4 0...1...3...3...2...8...7..10...6..12...9...21...4...17...39 A192787 .5 0...1...2...4...3...4...4...7..12..10...3...17...6...21...21 A226644 .6 0...1...1...3...3...3...1...6...8..10...7...10...1....9...12 A226645 .7 0...0...1...1...2...7...3...2...3...5...2...13...8...10....9 n/a .8 0...0...0...1...1...3...3...3...1...2...0....8...3....7...19 n/a .9 0...0...1...1...0...3...2...5...3...2...0....6...2....4...10 n/a 10 0...0...0...1...1...2...0...4...4...3...0....4...1....4....8 n/a Triangle (by antidiagonals): {3}, {1, 10}, {1, 3, 21}, {0, 3, 8, 28}, {0, 1, 3, 10, 36}, {0, 1, 3, 6, 12, 57}, ... MATHEMATICA f[m_, n_] := Length@ Solve[m/n == 1/x + 1/y + 1/z && 1 <= x <= y <= z, {x, y, z}, Integers]; Table[f[n, m - n + 1], {m, 12}, {n, m, 1, -1}] // Flatten CROSSREFS Cf. A227612, A226640, A226641, A226642, A192787, A226644, A226645. Sequence in context: A304638 A141903 A010289 * A347129 A127613 A211360 Adjacent sequences:  A226643 A226644 A226645 * A226647 A226648 A226649 KEYWORD nonn,tabl AUTHOR Allan C. Wechsler and Robert G. Wilson v, Aug 17 2013 STATUS approved

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Last modified May 28 05:47 EDT 2022. Contains 354112 sequences. (Running on oeis4.)