A307729 Sum of the smallest sides of all acute integer triangles with perimeter n.

0, 0, 1, 0, 1, 2, 1, 2, 4, 5, 4, 6, 8, 6, 13, 11, 18, 17, 19, 23, 22, 30, 29, 32, 37, 40, 54, 49, 63, 63, 65, 73, 79, 94, 90, 98, 113, 110, 138, 127, 151, 154, 161, 181, 180, 210, 209, 216, 240, 247, 279, 269, 297, 320, 318, 348, 359, 402, 396, 401, 441, 440

Offset: 1

Author

Wesley Ivan Hurt, May 15 2019

Keywords

• nonn

Links

• Wikipedia, Integer Triangle

Crossrefs

Cf. A070093.

Programs

Mathematica

Table[Sum[Sum[k*(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) = 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))) k.