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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, 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
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 15 2019
STATUS
approved