A308157 Sum of the perimeters of all integer-sided obtuse triangles with perimeter n.

0, 0, 0, 0, 0, 0, 7, 0, 9, 0, 22, 0, 26, 28, 45, 32, 51, 54, 95, 60, 147, 88, 184, 120, 225, 182, 270, 224, 319, 270, 434, 352, 528, 408, 630, 504, 703, 646, 819, 720, 943, 882, 1161, 968, 1350, 1104, 1504, 1296, 1666, 1500, 1887, 1716, 2120, 1890, 2420

Offset: 1

Author

Wesley Ivan Hurt, May 14 2019

Keywords

• nonn

Links

• Wikipedia, Integer Triangle

Crossrefs

Cf. A070101.

Programs

Mathematica

Table[n*Sum[Sum[ (1 - Sign[Floor[(i^2 + k^2)/(n - i - 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 * A070101(n).

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