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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A037020 A094878 A233401

Adjacent sequences:  A308230 A308231 A308232 * A308234 A308235 A308236

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 16 2019

STATUS

approved

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Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)