A307728 Sum of the perimeters of all acute integer triangles with perimeter n.

0, 0, 3, 0, 5, 6, 7, 8, 18, 20, 22, 24, 39, 28, 60, 48, 85, 72, 95, 100, 105, 132, 138, 144, 175, 182, 243, 224, 290, 270, 310, 320, 363, 408, 420, 432, 518, 494, 624, 560, 697, 672, 731, 792, 810, 920, 940, 960, 1078, 1100, 1224, 1196, 1325, 1404, 1430

Offset: 1

Author

Wesley Ivan Hurt, May 15 2019

Keywords

• nonn

Links

• Wikipedia, Integer Triangle

Crossrefs

Cf. A070093.

Programs

Mathematica

Table[n*Sum[Sum[(1 - Sign[Floor[(n - i - k)^2/(i^2 + k^2)]]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]

Formula

a(n) = n * A070093(n).

a(n) = n * Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} (1-sign(floor((n-i-k)^2/(i^2+k^2)))) * sign(floor((i+k)/(n-i-k+1))).