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A308202 Number of integer-sided triangles with perimeter n such that the length of the smallest side is coprime to n. 1
0, 0, 1, 0, 1, 0, 2, 0, 2, 1, 4, 0, 5, 1, 4, 2, 8, 2, 10, 1, 7, 4, 14, 4, 13, 6, 13, 4, 21, 3, 24, 9, 17, 11, 20, 7, 33, 13, 24, 13, 40, 9, 44, 13, 24, 20, 52, 15, 48, 19, 40, 20, 65, 18, 50, 27, 49, 33, 80, 21, 85, 37, 50, 40, 70, 24, 102, 37, 71, 32, 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(k,n) = 1], where [] is the Iverson bracket.

MATHEMATICA

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

CROSSREFS

Cf. A308074.

Sequence in context: A295689 A305804 A053470 * A329152 A337563 A278648

Adjacent sequences: A308199 A308200 A308201 * A308203 A308204 A308205

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 15 2019

STATUS

approved

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Last modified December 1 23:44 EST 2022. Contains 358485 sequences. (Running on oeis4.)