A308211 Number of integer-sided triangles with perimeter n and sides a, b and c such that a <= b <= c and the length of side a is coprime to c.

0, 0, 1, 0, 1, 0, 2, 1, 1, 1, 4, 2, 3, 1, 4, 4, 6, 4, 8, 5, 5, 4, 10, 7, 10, 8, 14, 12, 15, 10, 15, 11, 13, 12, 20, 17, 21, 16, 24, 22, 27, 22, 30, 24, 27, 25, 37, 30, 34, 28, 37, 34, 40, 32, 42, 38, 42, 39, 54, 46, 53, 45, 59, 56, 63, 57, 69, 60, 65, 60, 74

Offset

1,7

Links

Table of n, a(n) for n=1..71.

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

Mathematica

Table[Sum[Sum[Floor[1/GCD[k, 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. A308209.

Sequence in context: A100092 A131508 A305502 * A140130 A337087 A321312

Adjacent sequences: A308208 A308209 A308210 * A308212 A308213 A308214

Keyword

nonn

Author

Wesley Ivan Hurt, May 15 2019

Status

approved