A335208 Number of Heronian triangles with perimeter A335101(n) whose middle side length is a square.

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, 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, 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

Offset

1,9

Links

Table of n, a(n) for n=1..94.

Eric Weisstein's World of Mathematics, Heronian Triangle

Wikipedia, Heronian triangle

Wikipedia, Integer Triangle

Formula

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.

Example

a(1) = 1; There is one Heronian triangle with perimeter A335101(1) = 12 whose middle side length is a square, [3,4,5].

Crossrefs

Cf. A010052, A335101, A335191, A335211.

Sequence in context: A287056 A098357 A370958 * A165735 A083888 A102681

Adjacent sequences: A335205 A335206 A335207 * A335209 A335210 A335211

Keyword

nonn

Author

Wesley Ivan Hurt, May 26 2020

Status

approved