|
%I #8 Jun 16 2020 14:34:04
%S 0,0,3,0,0,0,0,0,9,0,0,12,0,0,0,0,0,0,19,0,0,22,0,0,0,0,27,0,0,0,0,0,
%T 33,34,0,36,0,0,0,0,41,0,0,0,0,0,0,48,0,0,51,0,0,54,0,0,57,0,59,0,0,0,
%U 0,0,0,66,0,0,0,0,0,0,73,0,75,76,77,0,0,0
%N Sum of the perimeters of the integer-sided triangles with perimeter n whose sides lengths are square numbers.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>
%F a(n) = n * Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * A010052(i) * A010052(k) * A010052(n-i-k).
%F a(n) = n * A308064(n).
%t Table[n*Sum[Sum[(Floor[Sqrt[i]] - Floor[Sqrt[i - 1]]) (Floor[Sqrt[k]] - Floor[Sqrt[k - 1]]) (Floor[Sqrt[n - k - i]] - Floor[Sqrt[n - k - i - 1]])*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
%Y Cf. A010052, A308064.
%K nonn
%O 1,3
%A _Wesley Ivan Hurt_, May 18 2019
|
