A308455 Number of integer-sided triangles with perimeter n and side lengths a, b and c such that a <= b <= c, and b is squarefree.

0, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 1, 3, 3, 6, 5, 7, 6, 7, 5, 7, 5, 7, 5, 7, 6, 9, 8, 12, 12, 16, 15, 19, 17, 21, 19, 23, 21, 26, 23, 27, 25, 29, 26, 31, 28, 33, 30, 35, 32, 37, 33, 38, 35, 40, 37, 42, 39, 44, 41, 47, 45, 52, 49, 55, 52, 58, 54, 61, 57, 64, 60

Offset

1,7

Links

Table of n, a(n) for n=1..72.

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))) * mu(i)^2, where mu is the Möbius function (A008683).

Mathematica

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

Crossrefs

Cf. A008683, A308454.

Sequence in context: A259551 A058232 A216320 * A214716 A116933 A354060

Adjacent sequences: A308452 A308453 A308454 * A308456 A308457 A308458

Keyword

nonn

Author

Wesley Ivan Hurt, May 27 2019

Status

approved