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

1,3

Links

Table of n, a(n) for n=1..55.

Wikipedia, Integer Triangle

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))).

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}]

Crossrefs

Cf. A070093.

Sequence in context: A038556 A342303 A193508 * A263199 A052483 A308116

Adjacent sequences: A307725 A307726 A307727 * A307729 A307730 A307731

Keyword

nonn

Author

Wesley Ivan Hurt, May 15 2019

Status

approved