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A308143 Take all the integer-sided triangles with perimeter n and squarefree sides a, b, and c such that a <= b <= c. a(n) is the sum of all the b's. 0
0, 0, 1, 0, 2, 2, 5, 3, 3, 0, 8, 5, 16, 11, 29, 18, 18, 12, 13, 7, 23, 23, 51, 35, 28, 20, 62, 44, 82, 79, 132, 98, 100, 75, 144, 108, 121, 80, 185, 131, 148, 87, 203, 145, 265, 200, 345, 264, 300, 214, 272, 187, 305, 274, 301, 216, 246, 210, 340, 258, 406 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..61.

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

MATHEMATICA

Table[Sum[Sum[i* MoebiusMu[i]^2*MoebiusMu[k]^2*MoebiusMu[n - k - 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, A308116.

Sequence in context: A146316 A258803 A157495 * A308515 A128134 A157223

Adjacent sequences:  A308140 A308141 A308142 * A308144 A308145 A308146

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 14 2019

STATUS

approved

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Last modified August 8 08:27 EDT 2020. Contains 336293 sequences. (Running on oeis4.)