A307736 Sum of the largest sides of all acute integer triangles with perimeter n.

0, 0, 1, 0, 2, 2, 3, 3, 7, 8, 9, 9, 16, 11, 24, 19, 35, 28, 39, 40, 42, 53, 56, 57, 71, 73, 98, 90, 118, 107, 126, 128, 146, 164, 170, 172, 210, 198, 252, 224, 283, 268, 295, 318, 325, 370, 379, 384, 435, 442, 492, 480, 534, 563, 576, 606, 641, 699, 713, 694

Offset: 1

Author

Wesley Ivan Hurt, May 15 2019

Keywords

• nonn

Links

• Wikipedia, Integer Triangle

Crossrefs

Cf. A307729.

Programs

Mathematica

Table[Sum[Sum[(n - i - 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, 150}]

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))) * (n-i-k).