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A308234
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Take apart the sides of each of the integer-sided scalene triangles with perimeter n (at their vertices) and rearrange them orthogonally in 3-space so that their endpoints coincide at a single point. a(n) is the total volume of all rectangular prisms enclosed in this way.
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0
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0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 40, 60, 132, 90, 309, 266, 584, 570, 1013, 1018, 1939, 1678, 2866, 3062, 4603, 4382, 6991, 6818, 10038, 10068, 13988, 14140, 20137, 19308, 26397, 27260, 35652, 35196, 47075, 46836, 60591, 61004, 76824, 77616, 98981, 97350
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OFFSET
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1,9
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LINKS
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FORMULA
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a(n) = Sum_{k=1..floor((n-1)/3)} Sum_{i=k+1..floor((n-k-1)/2)} sign(floor((i+k)/(n-i-k+1))) * i * k * (n-i-k).
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MATHEMATICA
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Table[Sum[Sum[i*k*(n - i - k)*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k + 1, Floor[(n - k - 1)/2]}], {k, Floor[(n - 1)/3]}], {n, 100}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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