A308118 Number of obtuse integer-sided triangles with perimeter n and squarefree sides.

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 2, 1, 0, 0, 0, 0, 1, 2, 4, 3, 1, 0, 2, 1, 4, 5, 6, 5, 2, 2, 5, 3, 4, 3, 7, 4, 3, 2, 7, 4, 9, 8, 12, 10, 10, 8, 7, 5, 7, 7, 5, 4, 2, 4, 7, 7, 11, 12, 15, 12, 13, 13, 19, 12, 20, 20, 23, 18, 16, 16, 21, 18, 25, 27, 31

Offset

1,15

Links

Table of n, a(n) for n=1..79.

Wikipedia, Integer Triangle

Formula

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} (1-sign(floor((i^2+k^2)/(n-i-k)^2))) * sign(floor((i+k)/(n-i-k+1))) mu(i)^2 * mu(k)^2 * mu(n-i-k)^2, where mu is the Möbius function (A008683).

Mathematica

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

Crossrefs

Cf. A008683, A070093, A308117.

Sequence in context: A284499 A280457 A349903 * A017857 A127842 A127512

Adjacent sequences: A308115 A308116 A308117 * A308119 A308120 A308121

Keyword

nonn

Author

Wesley Ivan Hurt, May 13 2019

Status

approved