|
%I #11 Feb 01 2021 21:47:49
%S 1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,2,4,1,
%T 1,2,1,1,1,1,1,1,1,3,1,1,1,1,2,1,1,1,1,1,1,1,6,3,9,2,1,1,2,1,5,4,1,1,
%U 1,1,1,1,1,1,2,2,1,1,1,2,1,1,1,4,1,1,2,1,1,1,3,1,1,1
%N Number of Heronian triangles with perimeter A335101(n) whose middle side length is a square.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeronianTriangle.html">Heronian Triangle</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Heronian_triangle">Heronian triangle</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>
%F a(n) = Sum_{k=1..floor(b(n)/3)} Sum_{i=k..floor((b(n)-k)/2)} sign(floor((i+k)/(b(n)-i-k+1))) * chi(sqrt((b(n)/2)*(b(n)/2-i)*(b(n)/2-k)*(b(n)/2-(b(n)-i-k)))) * c(i), where chi(n) = 1 - ceiling(n) + floor(n), c is the square characteristic (A010052) and b = A335101.
%e a(1) = 1; There is one Heronian triangle with perimeter A335101(1) = 12 whose middle side length is a square, [3,4,5].
%Y Cf. A010052, A335101, A335191, A335211.
%K nonn
%O 1,9
%A _Wesley Ivan Hurt_, May 26 2020
|
