A308276 Sum of the smallest side lengths of all integer-sided triangles with perimeter n whose sides are square numbers.

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

Offset

1,12

Links

Table of n, a(n) for n=1..85.

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) * k.

Mathematica

Table[Sum[Sum[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, A308275.

Sequence in context: A308426 A308429 A308428 * A340977 A180989 A075444

Adjacent sequences: A308273 A308274 A308275 * A308277 A308278 A308279

Keyword

nonn

Author

Wesley Ivan Hurt, May 18 2019

Status

approved