A211381 Number of pairs of intersecting diagonals in the exterior of a regular n-gon.

0, 0, 0, 0, 7, 24, 63, 130, 242, 408, 650, 980, 1425, 2000, 2737, 3654, 4788, 6160, 7812, 9768, 12075, 14760, 17875, 21450, 25542, 30184, 35438, 41340, 47957, 55328, 63525, 72590, 82600, 93600, 105672, 118864, 133263, 148920, 165927, 184338, 204250, 225720

Offset

3,5

Links

Table of n, a(n) for n=3..44.

Eric Weisstein's World of Mathematics, Regular Polygon Division by Diagonals.

Index entries for linear recurrences with constant coefficients, signature (3,-1,-5,5,1,-3,1).

Formula

a(n) = 1/24*n*(n-4)*(n-6)*(2*n-7) for n even.

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

a(n) = A211380(n) - A000332(n).

G.f.: x^7*(2*x^2-3*x-7) / ((x-1)^5*(x+1)^2). [Colin Barker, Feb 14 2013]

Maple

a:= n-> `if`(n mod 2 = 0, 1/24*n*(n-4)*(n-6)*(2*n-7), 1/24*n*(n-3)*(n-5)*(2*n-11)): seq (a(n), n=3..40);

Crossrefs

Cf. A000332, A117662, A176145, A211380.

Sequence in context: A114291 A211382 A217746 * A339254 A305676 A101903

Adjacent sequences: A211378 A211379 A211380 * A211382 A211383 A211384

Keyword

nonn,easy

Author

Martin Renner, Feb 07 2013

Status

approved