A307737 Take all the integer-sided acute triangles with perimeter n and sides a, b, and c such that a <= b <= c. a(n) is the sum of all the b's.

0, 0, 1, 0, 2, 2, 3, 3, 7, 7, 9, 9, 15, 11, 23, 18, 32, 27, 37, 37, 41, 49, 53, 55, 67, 69, 91, 85, 109, 100, 119, 119, 138, 150, 160, 162, 195, 186, 234, 209, 263, 250, 275, 293, 305, 340, 352, 360, 403, 411, 453, 447, 494, 521, 536, 558, 596, 639, 661, 645

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))) i.

Mathematica

Table[Sum[Sum[i*(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. A307736.

Sequence in context: A133076 A295510 A324520 * A309684 A330950 A032060

Adjacent sequences: A307734 A307735 A307736 * A307738 A307739 A307740

Keyword

nonn

Author

Wesley Ivan Hurt, May 15 2019

Status

approved