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%I #9 Jun 18 2020 13:54:56
%S 0,0,0,0,1,1,2,1,2,2,4,2,5,4,7,5,8,7,9,8,12,9,14,12,16,14,18,16,21,19,
%T 24,21,26,23,30,26,33,30,37,33,39,37,44,40,48,44,52,47,56,52,60,56,65,
%U 60,70,65,74,70,79,75,85,80,91,85,96,90,102,96,108
%N Number of integer-sided triangles with perimeter n and at least one nonsquare side length.
%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)} sign(floor((i+k)/(n-i-k+1))) * (1 - A010052(i) * A010052(k) * A010052(n-i-k)).
%F a(n) = A005044(n) - A308064(n).
%t Table[Sum[Sum[(1 - (Floor[Sqrt[i]] - Floor[Sqrt[i - 1]]) (Floor[Sqrt[k]] - Floor[Sqrt[k - 1]]) (Floor[Sqrt[n - k - i]] - Floor[Sqrt[n - k - i - 1]]))*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
%Y Cf. A005044, A010052, A308064.
%K nonn
%O 1,7
%A _Wesley Ivan Hurt_, May 19 2019