A308209 - OEIS

A308209

Number of integer-sided triangles with perimeter n whose largest side length is coprime to n.

0, 0, 1, 0, 1, 0, 2, 1, 2, 0, 4, 2, 5, 1, 4, 3, 8, 2, 10, 5, 7, 3, 14, 5, 13, 5, 13, 9, 21, 7, 24, 12, 17, 9, 20, 10, 33, 12, 24, 15, 40, 13, 44, 22, 24, 18, 52, 18, 48, 22, 40, 30, 65, 21, 50, 31, 49, 30, 80, 19, 85, 35, 50, 45, 70, 32, 102, 51, 71, 42, 114

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

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

MATHEMATICA

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

CROSSREFS

Cf. A308202.