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A308211
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 c.
1
0, 0, 1, 0, 1, 0, 2, 1, 1, 1, 4, 2, 3, 1, 4, 4, 6, 4, 8, 5, 5, 4, 10, 7, 10, 8, 14, 12, 15, 10, 15, 11, 13, 12, 20, 17, 21, 16, 24, 22, 27, 22, 30, 24, 27, 25, 37, 30, 34, 28, 37, 34, 40, 32, 42, 38, 42, 39, 54, 46, 53, 45, 59, 56, 63, 57, 69, 60, 65, 60, 74
OFFSET
1,7
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,n-i-k) = 1], where [] is the Iverson bracket.
MATHEMATICA
Table[Sum[Sum[Floor[1/GCD[k, 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. A308209.
Sequence in context: A100092 A131508 A305502 * A140130 A337087 A321312
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 15 2019
STATUS
approved