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

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

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) - A070081(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, 3]] (* Jean-François Alcover, Jul 09 2017 *)

Crossrefs

Cf. A046130, A055592, A069598, A069597.

Cf. A070080, A070081, A070083, A070084, A070085, A070086.

Sequence in context: A211190 A072644 A179864 * A085727 A343005 A143442

Adjacent sequences: A070079 A070080 A070081 * A070083 A070084 A070085

Keyword

nonn

Author

Reinhard Zumkeller, May 05 2002

Status

approved