A308210 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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.