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%I #31 Oct 04 2021 08:23:13
%S 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,
%T 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,
%U 9,8,8,7,10,10,10,9,10,9,10,9,8,9,8,7,10,10
%N Largest side of integer triangles [A070080(n) <= A070081(n) <= a(n)], sorted by perimeter, sides lexicographically ordered.
%H G. C. Greubel, <a href="/A070082/b070082.txt">Table of n, a(n) for the first 55 rows, flattened</a>
%H Reinhard Zumkeller, <a href="/A070080/a070080.txt">Integer-sided triangles</a>
%F a(n) = A070083(n) - A070080(n) - A070081(n).
%t m = 55 (* max perimeter *);
%t sides[per_] := Select[Reverse /@ IntegerPartitions[per, {3}, Range[ Ceiling[per/2]]], #[[1]] < per/2 && #[[2]] < per/2 && #[[3]] < per/2&];
%t triangles = DeleteCases[Table[sides[per], {per, 3, m}], {}] // Flatten[#, 1]& // SortBy[Total[#] m^3 + #[[1]] m^2 + #[[2]] m + #[[1]]&];
%t triangles[[All, 3]] (* _Jean-François Alcover_, Jul 09 2017 *)
%Y Cf. A046130, A055592, A069598, A069597.
%Y Cf. A070080, A070081, A070083, A070084, A070085, A070086.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, May 05 2002
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