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%I #43 Sep 17 2020 16:16:53
%S 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,
%T 90,118,107,126,128,146,164,170,172,210,198,252,224,283,268,295,318,
%U 325,370,379,384,435,442,492,480,534,563,576,606,641,699,713,694
%N Sum of the largest sides of all acute integer 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((n-i-k)^2/(i^2+k^2)))) * sign(floor((i+k)/(n-i-k+1))) * (n-i-k).
%t 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}]
%Y Cf. A307729.
%K nonn
%O 1,5
%A _Wesley Ivan Hurt_, May 15 2019
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