A308233 Take apart the sides of each of the integer-sided 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, 1, 0, 4, 8, 21, 18, 67, 68, 158, 174, 323, 358, 703, 658, 1150, 1310, 2008, 2018, 3269, 3338, 4977, 5192, 7292, 7630, 10967, 10836, 14931, 15836, 20856, 21084, 28373, 28836, 37506, 38492, 48708, 50076, 64140, 64086, 80326, 83224, 101970, 103026, 127680

Offset

1,5

Links

Table of n, a(n) for n=1..45.

Wikipedia, Integer Triangle

Formula

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/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, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]

Crossrefs

Cf. A005044.

Sequence in context: A000585 A209451 A102559 * A371001 A037020 A094878

Adjacent sequences: A308230 A308231 A308232 * A308234 A308235 A308236

Keyword

nonn

Author

Wesley Ivan Hurt, May 16 2019

Status

approved