A211383 Number of intersections of diagonals in the interior and exterior of a regular n-gon.

0, 1, 5, 13, 42, 73, 189, 271, 572, 661, 1365, 1569, 2790, 3057, 5117, 4555, 8664, 9041, 13797, 14213, 20930, 18625, 30525, 30967, 43092, 43513, 59189

Offset

3,3

Links

Table of n, a(n) for n=3..29.

Bjorn Poonen and Michael Rubinstein, The Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics 11 (1998), nr. 1, pp. 135-156; doi: 10.1137/S0895480195281246; arXiv: math.MG/9508209.

Eric W. Weisstein, MathWorld: Regular Polygon Division by Diagonals

Formula

a(n) = 1/8*n*(n-3)*(n^2-8*n+19) for n odd.

a(n) = A006561(n) + A211382(n).

Crossrefs

Cf. A006561, A211382.

Sequence in context: A111009 A012172 A316536 * A066873 A105262 A298234

Adjacent sequences: A211380 A211381 A211382 * A211384 A211385 A211386

Keyword

nonn,more

Author

Martin Renner, Feb 07 2013

Status

approved