A308277 Sum of the largest side lengths of all integer-sided triangles with perimeter n whose sides are square numbers.

0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 9, 0, 0, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 16, 16, 0, 16, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 16, 0, 0, 25, 0, 0, 25, 0, 0, 25, 0, 25, 0, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 0, 36, 0, 25, 36, 36, 0, 0, 0, 36

Offset

1,9

Links

Table of n, a(n) for n=1..81.

Wikipedia, Integer Triangle

Formula

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * A010052(i) * A010052(k) * A010052(n-i-k) * (n-i-k).

Mathematica

Table[Sum[Sum[(n - i - k) (Floor[Sqrt[i]] - Floor[Sqrt[i - 1]]) (Floor[Sqrt[k]] - Floor[Sqrt[k - 1]]) (Floor[Sqrt[n - k - i]] - Floor[Sqrt[n - k - i - 1]])*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]

Crossrefs

Cf. A010052, A308276.

Sequence in context: A050443 A306770 A308278 * A278216 A036480 A035639

Adjacent sequences: A308274 A308275 A308276 * A308278 A308279 A308280

Keyword

nonn

Author

Wesley Ivan Hurt, May 18 2019

Status

approved