|
%I #38 Jun 16 2020 14:51:57
%S 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,
%T 85,109,100,119,119,138,150,160,162,195,186,234,209,263,250,275,293,
%U 305,340,352,360,403,411,453,447,494,521,536,558,596,639,661,645
%N 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.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>
%F 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.
%t 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}]
%Y Cf. A307736.
%K nonn
%O 1,5
%A _Wesley Ivan Hurt_, May 15 2019
|
