A335211 Number of Heronian triangles with perimeter A335104(n) whose largest side length is a square.

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 2, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 3, 1, 1, 2, 2, 1, 2, 1, 1, 1, 2, 5, 2, 1, 1, 1, 1, 1, 4

Offset

1,9

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

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(b(n)-i-k), where chi(n) = 1 - ceiling(n) + floor(n), c is the square characteristic (A010052) and b = A335104.

Crossrefs

Cf. A010052, A335104, A335191, A335208.

Sequence in context: A274274 A072550 A037810 * A038769 A327818 A255481

Adjacent sequences: A335208 A335209 A335210 * A335212 A335213 A335214

Keyword

nonn

Author

Wesley Ivan Hurt, May 26 2020

Status

approved