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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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%I #34 Oct 04 2021 08:17:25

%S 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,

%T 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,

%U 6,7,6,7,10,9,8,9,7,8,6,7,8,6,7,7,10,9,8,9,7

%N Middle side of integer triangles [A070080(n) <= a(n) <= A070082(n)], sorted by perimeter, sides lexicographically ordered.

%H G. C. Greubel, <a href="/A070081/b070081.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) - A070082(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, 2]] (* _Jean-François Alcover_, Jul 09 2017 *)

%Y Cf. A046129, A055593, A069595, A069594, A069598.

%Y Cf. A070080, A070082, A070083, A070084, A070085, A070086.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, May 05 2002