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A308213

Number of integer-sided triangles with perimeter n and sides a, b and c such that a <= b <= c and the length of side b is coprime to c.

0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 2, 1, 2, 1, 4, 3, 4, 3, 5, 3, 5, 5, 9, 7, 8, 6, 11, 9, 11, 9, 13, 10, 13, 12, 18, 16, 18, 15, 23, 21, 23, 20, 24, 20, 24, 22, 31, 27, 30, 27, 36, 33, 37, 33, 41, 37, 41, 39, 50, 45, 47, 42, 55, 51, 56, 52, 60, 54, 60, 57, 67, 61

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OFFSET

1,11

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))) * [gcd(i,n-i-k) = 1], where [] is the Iverson bracket.

MATHEMATICA

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

CROSSREFS

Cf. A308212.