A308234 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.

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

Offset

1,9

Links

Table of n, a(n) for n=1..46.

Wikipedia, Integer Triangle

Formula

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).

Mathematica

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}]

Crossrefs

Cf. A308233.

Sequence in context: A075406 A075404 A356304 * A362795 A242837 A353324

Adjacent sequences: A308231 A308232 A308233 * A308235 A308236 A308237

Keyword

nonn

Author

Wesley Ivan Hurt, May 16 2019

Status

approved