A308118 Number of obtuse integer-sided triangles with perimeter n and squarefree sides.
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 2, 1, 0, 0, 0, 0, 1, 2, 4, 3, 1, 0, 2, 1, 4, 5, 6, 5, 2, 2, 5, 3, 4, 3, 7, 4, 3, 2, 7, 4, 9, 8, 12, 10, 10, 8, 7, 5, 7, 7, 5, 4, 2, 4, 7, 7, 11, 12, 15, 12, 13, 13, 19, 12, 20, 20, 23, 18, 16, 16, 21, 18, 25, 27, 31
Offset: 1
Keywords
Links
- Wikipedia, Integer Triangle
Programs
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Mathematica
Table[Sum[Sum[MoebiusMu[i]^2*MoebiusMu[k]^2*MoebiusMu[n - k - i]^2 (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}]
Formula
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))) mu(i)^2 * mu(k)^2 * mu(n-i-k)^2, where mu is the Möbius function (A008683).