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

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.

Sequence in context: A160595 A105778 A344245 * A226279 A344246 A344254

Adjacent sequences: A308210 A308211 A308212 * A308214 A308215 A308216

Keyword

nonn

Author

Wesley Ivan Hurt, May 15 2019

Status

approved