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

1, 1, 2, 1, 2, 2, 1, 2, 3, 2, 3, 1, 2, 3, 3, 2, 3, 4, 1, 2, 3, 3, 4, 2, 3, 4, 4, 1, 2, 3, 3, 4, 4, 5, 2, 3, 4, 4, 5, 1, 2, 3, 3, 4, 4, 5, 5, 2, 3, 4, 4, 5, 5, 6, 1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 2, 3, 4, 4, 5, 5, 6, 6, 1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 2, 3, 4, 4, 5, 5

Offset

1,3

Links

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

Reinhard Zumkeller, Integer-sided triangles

Formula

a(n) = A070083(n) - A070082(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, 1]] (* Jean-François Alcover, Jun 12 2012, updated Jul 09 2017 *)

Crossrefs

Cf. A046128, A055594, A069597.

Cf. A070081, A070082, A070083, A070084, A070085, A070086.

Cf. A316841, A316843, A316844, A316845 (sides (i,j,k) with j + k > i >= j >= k >= 1).

Cf. A331244, A331245, A331246 (similar, but triangles sorted by radius of enclosing circle), A331251, A331252, A331253 (triangles sorted by area), A331254, A331255, A331256 (triangles sorted by radius of circumcircle).

Sequence in context: A282518 A230241 A029315 * A230196 A131400 A132749

Adjacent sequences: A070077 A070078 A070079 * A070081 A070082 A070083

Keyword

nonn

Author

Reinhard Zumkeller, May 05 2002

Status

approved