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A070082 Largest side of integer triangles [A070080(n) <= A070081(n) <= a(n)], sorted by perimeter, sides lexicographically ordered. 73
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 February 22 19:56 EST 2019. Contains 320403 sequences. (Running on oeis4.)