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 A193866 #34 Sep 08 2022 08:45:58
%S A193866 0,6,11,35,46,88,105,165,188,266,295,391,426,540,581,713,760,910,963,
%T A193866 1131,1190,1376,1441,1645,1716,1938,2015,2255,2338,2596,2685,2961,
%U A193866 3056,3350,3451,3763,3870,4200,4313,4661,4780,5146,5271,5655,5786,6188
%N A193866 Even pentagonal numbers divided by 2.
%H A193866 Harvey P. Dale, <a href="/A193866/b193866.txt">Table of n, a(n) for n = 0..1000</a>
%H A193866 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A193866 a(n) = 1/16*(1-3*(-1)^n+12*n)*(1-(-1)^n+4*n).
%F A193866 a(n) = A014633(n)/2.
%F A193866 a(0)=0, a(1)=6, a(2)=11, a(3)=35, a(4)=46, a(n)=a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5). G.f.: x*(6+5*x+12*x^2+x^3)/(1-x-2*x^2+2*x^3+x^4-x^5). [_Colin Barker_, Jan 25 2012]
%t A193866 Table[(1/16 (1 - 3 (-1)^n + 12 n) (1 - (-1)^n + 4 n)), {n, 0, 50}] (* _Vincenzo Librandi_, Jun 20 2015 *)
%t A193866 Select[PolygonalNumber[5,Range[0,100]],EvenQ]/2 (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 13 2018 *)
%o A193866 (PARI) a(n)=3*n^2+if(n%2,5*n+1,-n)/2 \\ _Charles R Greathouse IV_, Aug 18 2011
%o A193866 (Magma) [1/16*(1-3*(-1)^n+12*n)*(1-(-1)^n+4*n): n in [0..60]]; // _Vincenzo Librandi_, Jun 20 2015
%Y A193866 Cf. A000326, A001105, A033991.
%K A193866 nonn,easy
%O A193866 0,2
%A A193866 _Omar E. Pol_, Aug 18 2011