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