A308214 Sum of the smallest side lengths of all integer-sided obtuse triangles with perimeter n.
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, 57, 54, 82, 68, 98, 77, 117, 97, 127, 127, 148, 138, 171, 169, 211, 181, 246, 206, 271, 246, 298, 285, 334, 325, 378, 354, 437, 385, 481, 423, 529, 489, 574, 565
Offset: 1
Keywords
Links
- Wikipedia, Integer Triangle
Crossrefs
Cf. A308157.
Programs
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Mathematica
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}]
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))) k.