A308212 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 b.

0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 2, 2, 4, 2, 3, 2, 5, 3, 6, 6, 8, 4, 8, 7, 10, 6, 9, 8, 13, 11, 16, 15, 18, 12, 16, 15, 21, 15, 19, 17, 24, 20, 27, 26, 30, 22, 30, 29, 36, 30, 35, 33, 42, 36, 42, 40, 46, 36, 46, 44, 54, 44, 50, 47, 55, 49, 60, 58, 65, 57, 69

Offset

1,9

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,i) = 1], where [] is the Iverson bracket.

Mathematica

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

Crossrefs

Cf. A308211.

Sequence in context: A157898 A137430 A262138 * A181346 A300815 A358933

Adjacent sequences: A308209 A308210 A308211 * A308213 A308214 A308215

Keyword

nonn

Author

Wesley Ivan Hurt, May 15 2019

Status

approved