A308210 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 n.

0, 0, 1, 0, 1, 0, 2, 1, 1, 1, 4, 1, 5, 2, 2, 3, 8, 3, 10, 4, 4, 5, 14, 3, 13, 7, 12, 8, 21, 6, 24, 11, 12, 12, 20, 10, 33, 15, 18, 12, 40, 12, 44, 20, 28, 22, 52, 15, 48, 21, 32, 28, 65, 21, 50, 26, 40, 35, 80, 20, 85, 40, 56, 43, 70, 30, 102, 48, 60, 34

Offset

1,7

Links

Table of n, a(n) for n=1..70.

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

Mathematica

Table[Sum[Sum[Floor[1/GCD[i, n]] 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: A348647 A254048 A306671 * A112331 A133910 A345938

Adjacent sequences: A308207 A308208 A308209 * A308211 A308212 A308213

Keyword

nonn

Author

Wesley Ivan Hurt, May 15 2019

Status

approved