A070081 Middle side of integer triangles [A070080(n) <= a(n) <= A070082(n)], sorted by perimeter, sides lexicographically ordered.

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

Offset: 1

Author

Reinhard Zumkeller, May 05 2002

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for the first 55 rows, flattened
• Reinhard Zumkeller, Integer-sided triangles

Crossrefs

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

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

Programs

Mathematica

m = 55 (* max perimeter *);
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 *)

Formula

a(n) = A070083(n) - A070080(n) - A070082(n).