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 A070082 Largest side of integer triangles [A070080(n) <= A070081(n) <= a(n)], sorted by perimeter, sides lexicographically ordered. 74
 1, 2, 2, 3, 3, 3, 4, 4, 3, 4, 4, 5, 5, 5, 4, 5, 5, 4, 6, 6, 6, 5, 5, 6, 6, 6, 5, 7, 7, 7, 6, 7, 6, 5, 7, 7, 7, 6, 6, 8, 8, 8, 7, 8, 7, 7, 6, 8, 8, 8, 7, 8, 7, 6, 9, 9, 9, 8, 9, 8, 9, 8, 7, 7, 9, 9, 9, 8, 9, 8, 8, 7, 10, 10, 10, 9, 10, 9, 10, 9, 8, 9, 8, 7, 10, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A070080(n) + A070081(n) + a(n) = A070083(n). LINKS G. C. Greubel, Table of n, a(n) for the first 55 rows, flattened R. Zumkeller, Integer-sided triangles MATHEMATICA maxPer = 22; maxSide = Floor[(maxPer-1)/2]; order[{a_, b_, c_}] := (a+b+c)*maxPer^3 + a*maxPer^2 + b*maxPer + c; triangles = Reap[Do[If[ a+b+c <= maxPer && c-b < a < c+b && b-a < c < b+a && c-a < b < c+a, Sow[{a, b, c}]], {a, 1, maxSide}, {b, a, maxSide}, {c, b, maxSide}]][[2, 1]]; Sort[triangles, order[#1] < order[#2] &] [[All, 3]](* Jean-François Alcover, Jun 12 2012 *) maxPer = m = 22; sides[per_] := Select[Reverse /@ IntegerPartitions[per, {3}, Range[Ceiling[per/2]]], #[[1]] < per/2 && #[[2]] < per/2 && #[[3]] < per/2&]; triangles = DeleteCases[Table[sides[per], {per, 3, m}], {}] // Flatten[#, 1]& // SortBy[Total[#] m^3 + #[[1]] m^2 + #[[2]] m + #[[1]]&]; triangles[[All, 3]] (* Jean-François Alcover, Jul 09 2017 *) CROSSREFS Cf. A046130, A070084, A070085, A070086, A055592, A069598, A069597. Sequence in context: A211190 A072644 A179864 * A085727 A143442 A137300 Adjacent sequences:  A070079 A070080 A070081 * A070083 A070084 A070085 KEYWORD nonn AUTHOR Reinhard Zumkeller, May 05 2002 STATUS approved

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Last modified August 13 00:27 EDT 2020. Contains 336441 sequences. (Running on oeis4.)