This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A211381 #20 Feb 16 2025 08:33:17 %S A211381 0,0,0,0,7,24,63,130,242,408,650,980,1425,2000,2737,3654,4788,6160, %T A211381 7812,9768,12075,14760,17875,21450,25542,30184,35438,41340,47957, %U A211381 55328,63525,72590,82600,93600,105672,118864,133263,148920,165927,184338,204250,225720 %N A211381 Number of pairs of intersecting diagonals in the exterior of a regular n-gon. %H A211381 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RegularPolygonDivisionbyDiagonals.html">Regular Polygon Division by Diagonals</a>. %H A211381 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-5,5,1,-3,1). %F A211381 a(n) = 1/24*n*(n-4)*(n-6)*(2*n-7) for n even. %F A211381 a(n) = 1/24*n*(n-3)*(n-5)*(2*n-11) for n odd. %F A211381 a(n) = A211380(n) - A000332(n). %F A211381 G.f.: x^7*(2*x^2-3*x-7) / ((x-1)^5*(x+1)^2). [_Colin Barker_, Feb 14 2013] %p A211381 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); %Y A211381 Cf. A000332, A117662, A176145, A211380. %K A211381 nonn,easy %O A211381 3,5 %A A211381 _Martin Renner_, Feb 07 2013