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 A335208 Number of Heronian triangles with perimeter A335101(n) whose middle side length is a square. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 LINKS 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: A030407 A287056 A098357 * A165735 A083888 A102681 Adjacent sequences:  A335205 A335206 A335207 * A335209 A335210 A335211 KEYWORD nonn AUTHOR Wesley Ivan Hurt, May 26 2020 STATUS approved

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Last modified May 22 10:56 EDT 2022. Contains 353949 sequences. (Running on oeis4.)