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A308225 Take the integer-sided triangles with perimeter n and mutually coprime sides a, b and c such that a <= b <= c. a(n) is the sum of all the b's. 0
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 5, 5, 0, 13, 0, 14, 7, 8, 7, 42, 9, 17, 29, 49, 20, 87, 11, 59, 22, 57, 37, 153, 24, 94, 82, 171, 58, 239, 62, 185, 79, 184, 81, 384, 106, 283, 163, 333, 91, 484, 156, 400, 181, 365, 166, 840, 218, 479, 385, 660, 280 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

LINKS

Table of n, a(n) for n=1..65.

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

MATHEMATICA

Table[Sum[Sum[i*Floor[1/(GCD[i, k]*GCD[i, n - i - k]*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. A308224.

Sequence in context: A005397 A259124 A273515 * A021718 A193108 A212044

Adjacent sequences:  A308222 A308223 A308224 * A308226 A308227 A308228

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 16 2019

STATUS

approved

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Last modified December 4 09:43 EST 2021. Contains 349485 sequences. (Running on oeis4.)