A307737 Take all the integer-sided acute 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, 1, 0, 2, 2, 3, 3, 7, 7, 9, 9, 15, 11, 23, 18, 32, 27, 37, 37, 41, 49, 53, 55, 67, 69, 91, 85, 109, 100, 119, 119, 138, 150, 160, 162, 195, 186, 234, 209, 263, 250, 275, 293, 305, 340, 352, 360, 403, 411, 453, 447, 494, 521, 536, 558, 596, 639, 661, 645
Offset: 1
Keywords
Links
- Wikipedia, Integer Triangle
Crossrefs
Cf. A307736.
Programs
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Mathematica
Table[Sum[Sum[i*(1 - Sign[Floor[(n - i - k)^2/(i^2 + k^2)]]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 150}]
Formula
a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} (1-sign(floor((n-i-k)^2/(i^2+k^2)))) * sign(floor((i+k)/(n-i-k+1))) i.