A308218 Take the integer-sided obtuse triangles with perimeter n and sides a, b and c such that a <= b <= c. a(n) is the sum of all the b's.
0, 0, 0, 0, 0, 0, 2, 0, 3, 0, 7, 0, 9, 9, 15, 11, 18, 18, 32, 21, 51, 30, 64, 41, 79, 62, 95, 77, 113, 93, 151, 124, 186, 144, 221, 177, 249, 225, 289, 253, 333, 310, 411, 343, 479, 390, 534, 456, 593, 527, 674, 605, 756, 667, 859, 733, 954, 826, 1049, 936
Offset: 1
Keywords
Links
- Wikipedia, Integer Triangle
Crossrefs
Cf. A308216.
Programs
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Mathematica
Table[Sum[Sum[i (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))) i.