A308216 Sum of the largest side lengths of all integer-sided obtuse triangles with perimeter n.

0, 0, 0, 0, 0, 0, 3, 0, 4, 0, 10, 0, 12, 12, 21, 14, 24, 24, 44, 27, 67, 40, 85, 54, 104, 82, 126, 101, 149, 123, 201, 160, 244, 187, 292, 230, 327, 294, 382, 329, 439, 403, 539, 444, 625, 508, 699, 594, 775, 688, 879, 786, 986, 869, 1124, 954, 1244, 1071

Offset

1,7

Links

Table of n, a(n) for n=1..58.

Wikipedia, Integer Triangle

Formula

a(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))) (n-i-k).

Mathematica

Table[Sum[Sum[(n - i - k) (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. A308214.

Sequence in context: A289445 A237558 A060034 * A035544 A129718 A127375

Adjacent sequences: A308213 A308214 A308215 * A308217 A308218 A308219

Keyword

nonn

Author

Wesley Ivan Hurt, May 15 2019

Status

approved