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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Table of n, a(n) for n=1..62.

Wikipedia, Integer Triangle

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

Adjacent sequences:  A307726 A307727 A307728 * A307730 A307731 A307732

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 15 2019

STATUS

approved

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Last modified January 15 09:30 EST 2021. Contains 340187 sequences. (Running on oeis4.)