cp's OEIS Frontend

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.

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

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%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