OFFSET
3,3
COMMENTS
A diagonal is parallel to an edge if and only if, on at least one side of the diagonal, there is an odd number of edges.
If n is odd, all of the diagonals of the n-gon are parallel to an edge.
LINKS
Paolo Xausa, Table of n, a(n) for n = 3..10000
Thomas Andrews, Number of Parallel/Not Parallel Diagonals of a Regular Polygon, Mathematics Stack Exchange, 2014.
Paolo Xausa, Illustration of first terms.
Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).
FORMULA
a(n) = n(n-3)/2 = A000096(n-3) if n is odd;
Sum_{n>=5} 1/a(n) = 59/36 - 2*log(2)/3. - Amiram Eldar, Dec 06 2024
MATHEMATICA
PROG
(Python)
def A367204(n): return n*(n-3)>>1 if n&1 else n*(n-4)>>2 # Chai Wah Wu, Nov 22 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paolo Xausa, Nov 10 2023
STATUS
approved