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A308117 Number of acute integer-sided triangles with perimeter n and squarefree sides. 1
0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 2, 1, 3, 2, 3, 2, 2, 1, 2, 1, 2, 1, 2, 2, 4, 3, 3, 2, 5, 3, 6, 4, 6, 5, 5, 3, 6, 5, 7, 4, 6, 5, 7, 4, 8, 5, 7, 4, 8, 5, 9, 7, 10, 7, 10, 6, 9, 5, 7, 6, 10, 7, 8, 6, 7, 7, 9, 7, 12, 9, 13, 11, 14, 10, 14, 11, 15, 13, 18, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,13

LINKS

Table of n, a(n) for n=1..82.

Wikipedia, Integer Triangle

FORMULA

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} (1-sign(floor((n-i-k)^2/(i^2+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[(n - i - k)^2/(i^2 + 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.

Sequence in context: A075256 A334523 A001480 * A270755 A305030 A110917

Adjacent sequences:  A308114 A308115 A308116 * A308118 A308119 A308120

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 13 2019

STATUS

approved

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Last modified May 15 02:21 EDT 2021. Contains 343909 sequences. (Running on oeis4.)