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A070081
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Middle side of integer triangles [A070080(n) <= a(n) <= A070082(n)], sorted by perimeter, sides lexicographically ordered.
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74
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1, 2, 2, 3, 2, 3, 4, 3, 3, 4, 3, 5, 4, 3, 4, 5, 4, 4, 6, 5, 4, 5, 4, 6, 5, 4, 5, 7, 6, 5, 6, 4, 5, 5, 7, 6, 5, 6, 5, 8, 7, 6, 7, 5, 6, 5, 6, 8, 7, 6, 7, 5, 6, 6, 9, 8, 7, 8, 6, 7, 5, 6, 7, 6, 9, 8, 7, 8, 6, 7, 6, 7, 10, 9, 8, 9, 7, 8, 6, 7, 8, 6, 7, 7, 10, 9, 8, 9, 7
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OFFSET
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1,2
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COMMENTS
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A070080(n) + a(n) + A070082(n) = A070083(n).
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LINKS
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G. C. Greubel, Table of n, a(n) for the first 55 rows, flattened
R. Zumkeller, Integer-sided triangles
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MATHEMATICA
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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, 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]]&]; triangles[[All, 2]] (* Jean-François Alcover, Jul 09 2017 *)
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CROSSREFS
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Cf. A046129, A070084, A070085, A070086, A055593, A069595, A069594, A069598.
Sequence in context: A340716 A181948 A238943 * A034883 A071647 A051125
Adjacent sequences: A070078 A070079 A070080 * A070082 A070083 A070084
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, May 05 2002
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STATUS
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approved
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