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A307737 Take all the integer-sided acute triangles with perimeter n and 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, 2, 2, 3, 3, 7, 7, 9, 9, 15, 11, 23, 18, 32, 27, 37, 37, 41, 49, 53, 55, 67, 69, 91, 85, 109, 100, 119, 119, 138, 150, 160, 162, 195, 186, 234, 209, 263, 250, 275, 293, 305, 340, 352, 360, 403, 411, 453, 447, 494, 521, 536, 558, 596, 639, 661, 645 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..60.

Wikipedia, Integer Triangle

FORMULA

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} (1-sign(floor((n-i-k)^2/(i^2+k^2)))) * sign(floor((i+k)/(n-i-k+1))) i.

MATHEMATICA

Table[Sum[Sum[i*(1 - Sign[Floor[(n - i - k)^2/(i^2 + k^2)]]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 150}]

CROSSREFS

Cf. A307736.

Sequence in context: A133076 A295510 A324520 * A309684 A330950 A032060

Adjacent sequences:  A307734 A307735 A307736 * A307738 A307739 A307740

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 15 2019

STATUS

approved

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Last modified January 27 05:36 EST 2021. Contains 340455 sequences. (Running on oeis4.)