A308216 - OEIS

%I #7 Jun 16 2020 14:31:29

%S 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,

%T 126,101,149,123,201,160,244,187,292,230,327,294,382,329,439,403,539,

%U 444,625,508,699,594,775,688,879,786,986,869,1124,954,1244,1071

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>

%F 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).

%t 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}]

%Y Cf. A308214.

%K nonn

%O 1,7

%A _Wesley Ivan Hurt_, May 15 2019