A308275 Sum of the perimeters of the integer-sided triangles with perimeter n whose sides lengths are square numbers.

0, 0, 3, 0, 0, 0, 0, 0, 9, 0, 0, 12, 0, 0, 0, 0, 0, 0, 19, 0, 0, 22, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, 33, 34, 0, 36, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 48, 0, 0, 51, 0, 0, 54, 0, 0, 57, 0, 59, 0, 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, 0, 73, 0, 75, 76, 77, 0, 0, 0

Offset

1,3

Links

Table of n, a(n) for n=1..80.

Wikipedia, Integer Triangle

Formula

a(n) = 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).

a(n) = n * A308064(n).

Mathematica

Table[n*Sum[Sum[(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, A308064.

Sequence in context: A123074 A095269 A356302 * A308254 A111417 A007271

Adjacent sequences: A308272 A308273 A308274 * A308276 A308277 A308278

Keyword

nonn

Author

Wesley Ivan Hurt, May 18 2019

Status

approved