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 A054876 Number of pairwise incongruent triangles with integer sides and positive integer area and second longest side of length n. 2
 0, 0, 0, 1, 2, 0, 0, 1, 0, 3, 0, 2, 4, 1, 4, 1, 4, 0, 0, 6, 1, 0, 0, 3, 10, 5, 0, 4, 6, 6, 0, 1, 1, 7, 7, 2, 5, 1, 8, 10, 6, 2, 0, 2, 5, 0, 0, 3, 0, 13, 13, 14, 6, 0, 7, 5, 0, 8, 0, 14, 9, 1, 3, 1, 23, 3, 0, 13, 2, 9, 0, 6, 7, 9, 19, 4, 1, 12, 0, 14, 0, 8, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Amiram Eldar, Table of n, a(n) for n = 1..1000 EXAMPLE a(10) is 3 because there are three different integer-sided, integer-area triangles with middle side length 10, namely [9,10,17], [10,10,12], and [10,10,16]. MATHEMATICA okQ[x_, y_, z_] := If[x + y <=z, False, Module[{s = (x + y + z)/2}, IntegerQ[ Sqrt[s(s-x)(s-y)(s-z)]]]]; a[n_] := Module[{num = 0}, Do[Do[If[okQ[x, n, z], num++], {x, 1, n}], {z, n, 2n}]; num]; Array[a, 100, 0] (* Amiram Eldar, Jun 19 2019 *) CROSSREFS Cf. A054875. Sequence in context: A182034 A171912 A306605 * A109502 A323887 A323365 Adjacent sequences:  A054873 A054874 A054875 * A054877 A054878 A054879 KEYWORD nonn AUTHOR Henry Bottomley, May 26 2000 EXTENSIONS Definition corrected and offset changed by James R. Buddenhagen, Jan 16 2012 More terms from Amiram Eldar, Jun 19 2019 STATUS approved

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Last modified June 14 20:21 EDT 2021. Contains 345038 sequences. (Running on oeis4.)