A308302 Number of integer-sided triangles with perimeter n and at least one nonsquare side length.

0, 0, 0, 0, 1, 1, 2, 1, 2, 2, 4, 2, 5, 4, 7, 5, 8, 7, 9, 8, 12, 9, 14, 12, 16, 14, 18, 16, 21, 19, 24, 21, 26, 23, 30, 26, 33, 30, 37, 33, 39, 37, 44, 40, 48, 44, 52, 47, 56, 52, 60, 56, 65, 60, 70, 65, 74, 70, 79, 75, 85, 80, 91, 85, 96, 90, 102, 96, 108

Offset

1,7

Links

Table of n, a(n) for n=1..69.

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))) * (1 - A010052(i) * A010052(k) * A010052(n-i-k)).

a(n) = A005044(n) - A308064(n).

Mathematica

Table[Sum[Sum[(1 - (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. A005044, A010052, A308064.

Sequence in context: A277891 A102722 A339219 * A225530 A020475 A156995

Adjacent sequences: A308299 A308300 A308301 * A308303 A308304 A308305

Keyword

nonn

Author

Wesley Ivan Hurt, May 19 2019

Status

approved