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%I #9 Jun 16 2020 14:30:53
%S 0,0,0,0,0,0,2,0,2,0,5,0,5,7,9,7,9,12,19,12,29,18,35,25,42,38,49,46,
%T 57,54,82,68,98,77,117,97,127,127,148,138,171,169,211,181,246,206,271,
%U 246,298,285,334,325,378,354,437,385,481,423,529,489,574,565
%N Sum of the smallest 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))) k.
%t Table[Sum[Sum[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. A308157.
%K nonn
%O 1,7
%A _Wesley Ivan Hurt_, May 15 2019
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