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URL: https://oeis.org/A307728

⇱ A307728 - OEIS

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A307728
Sum of the perimeters of all acute integer triangles with perimeter n.
0
0, 0, 3, 0, 5, 6, 7, 8, 18, 20, 22, 24, 39, 28, 60, 48, 85, 72, 95, 100, 105, 132, 138, 144, 175, 182, 243, 224, 290, 270, 310, 320, 363, 408, 420, 432, 518, 494, 624, 560, 697, 672, 731, 792, 810, 920, 940, 960, 1078, 1100, 1224, 1196, 1325, 1404, 1430
OFFSET
1,3
FORMULA
a(n) = n * A070093(n).
a(n) = 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))).
MATHEMATICA
Table[n*Sum[Sum[(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, 100}]
CROSSREFS
Cf. A070093.
Sequence in context: A038556 A342303 A193508 * A263199 A052483 A373775
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 15 2019
STATUS
approved