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

1,2

Links

G. C. Greubel, Table of n, a(n) for the first 55 rows, flattened

Reinhard Zumkeller, Integer-sided triangles

Formula

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

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 *)

Crossrefs

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

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

Sequence in context: A340716 A181948 A238943 * A366686 A071647 A034883

Adjacent sequences: A070078 A070079 A070080 * A070082 A070083 A070084

Keyword

nonn

Author

Reinhard Zumkeller, May 05 2002

Status

approved