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A308212 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 b. 1
0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 2, 2, 4, 2, 3, 2, 5, 3, 6, 6, 8, 4, 8, 7, 10, 6, 9, 8, 13, 11, 16, 15, 18, 12, 16, 15, 21, 15, 19, 17, 24, 20, 27, 26, 30, 22, 30, 29, 36, 30, 35, 33, 42, 36, 42, 40, 46, 36, 46, 44, 54, 44, 50, 47, 55, 49, 60, 58, 65, 57, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

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

MATHEMATICA

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

CROSSREFS

Cf. A308211.

Sequence in context: A157898 A137430 A262138 * A181346 A300815 A002121

Adjacent sequences:  A308209 A308210 A308211 * A308213 A308214 A308215

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 15 2019

STATUS

approved

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Last modified May 8 12:57 EDT 2021. Contains 343666 sequences. (Running on oeis4.)