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 A070083 Perimeters of integer triangles, sorted by perimeter, sides lexicographically ordered. 17
 3, 5, 6, 7, 7, 8, 9, 9, 9, 10, 10, 11, 11, 11, 11, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A005044(p) is the number of all integer triangles having perimeter p. LINKS R. Zumkeller, Integer-sided triangles FORMULA a(n) = A070080(n) + A070081(n) + A070082(n). MATHEMATICA maxPer = 19; 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]]; Total /@ Sort[triangles, order[#1] < order[#2] &] (* 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]]&]; Total /@ triangles (* Jean-François Alcover, Jul 09 2017 *) CROSSREFS Sequence in context: A317920 A305443 A122818 * A316851 A196778 A195770 Adjacent sequences:  A070080 A070081 A070082 * A070084 A070085 A070086 KEYWORD nonn AUTHOR Reinhard Zumkeller, May 05 2002 STATUS approved

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Last modified February 18 00:19 EST 2019. Contains 320237 sequences. (Running on oeis4.)