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

1,7

Links

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

Wikipedia, Integer Triangle

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))).

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}]

Crossrefs

Cf. A070101.

Sequence in context: A213186 A296482 A272429 * A198555 A234355 A021145

Adjacent sequences: A308154 A308155 A308156 * A308158 A308159 A308160

Keyword

nonn

Author

Wesley Ivan Hurt, May 14 2019

Status

approved