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%I #7 Jun 18 2020 13:45:07
%S 0,0,1,0,0,0,1,0,1,1,2,1,2,1,4,3,4,3,5,3,5,5,9,7,8,6,11,9,11,9,13,10,
%T 13,12,18,16,18,15,23,21,23,20,24,20,24,22,31,27,30,27,36,33,37,33,41,
%U 37,41,39,50,45,47,42,55,51,56,52,60,54,60,57,67,61
%N Number of integer-sided triangles with perimeter n and sides a, b and c such that a <= b <= c and the length of side b is coprime to c.
%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))) * [gcd(i,n-i-k) = 1], where [] is the Iverson bracket.
%t Table[Sum[Sum[Floor[1/GCD[i, n - i - k]] Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
%Y Cf. A308212.
%K nonn
%O 1,11
%A _Wesley Ivan Hurt_, May 15 2019
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