A307736 Sum of the largest sides of all acute integer triangles with perimeter n.

0, 0, 1, 0, 2, 2, 3, 3, 7, 8, 9, 9, 16, 11, 24, 19, 35, 28, 39, 40, 42, 53, 56, 57, 71, 73, 98, 90, 118, 107, 126, 128, 146, 164, 170, 172, 210, 198, 252, 224, 283, 268, 295, 318, 325, 370, 379, 384, 435, 442, 492, 480, 534, 563, 576, 606, 641, 699, 713, 694

Offset

1,5

Links

Table of n, a(n) for n=1..60.

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))) * (n-i-k).

Mathematica

Table[Sum[Sum[(n - i - 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, 150}]

Crossrefs

Cf. A307729.

Sequence in context: A330950 A032060 A241385 * A309713 A153903 A331729

Adjacent sequences: A307733 A307734 A307735 * A307737 A307738 A307739

Keyword

nonn

Author

Wesley Ivan Hurt, May 15 2019

Status

approved