login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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: 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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