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A307729
Sum of the smallest sides of all acute integer triangles with perimeter n.
1
0, 0, 1, 0, 1, 2, 1, 2, 4, 5, 4, 6, 8, 6, 13, 11, 18, 17, 19, 23, 22, 30, 29, 32, 37, 40, 54, 49, 63, 63, 65, 73, 79, 94, 90, 98, 113, 110, 138, 127, 151, 154, 161, 181, 180, 210, 209, 216, 240, 247, 279, 269, 297, 320, 318, 348, 359, 402, 396, 401, 441, 440
OFFSET
1,6
FORMULA
a(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))) k.
MATHEMATICA
Table[Sum[Sum[k*(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: A301364 A309503 A057061 * A245660 A034804 A050042
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 15 2019
STATUS
approved