A211382 Number of intersections of diagonals in the exterior of a regular n-gon.

0, 0, 0, 0, 7, 24, 63, 110, 242, 360, 650, 812, 1425, 1680, 2737, 2718, 4788, 5200, 7812, 8272, 12075, 11328, 17875, 18486, 25542, 26264, 35438

Offset

3,5

Links

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

Bjorn Poonen; 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 Weisstein, Regular Polygon Division by Diagonals (MathWorld).

Formula

a(n) = 1/24*n*(n-3)*(n-5)*(2*n-11) for n odd

Crossrefs

Cf. A006561.

Sequence in context: A002969 A029585 A114291 * A217746 A211381 A339254

Adjacent sequences: A211379 A211380 A211381 * A211383 A211384 A211385

Keyword

nonn,more

Author

Martin Renner, Feb 07 2013

Extensions

a(17)-a(29) from Martin Renner, Feb 24 2013

Status

approved