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 A014633 #48 Jan 13 2024 03:33:27
%S A014633 0,12,22,70,92,176,210,330,376,532,590,782,852,1080,1162,1426,1520,
%T A014633 1820,1926,2262,2380,2752,2882,3290,3432,3876,4030,4510,4676,5192,
%U A014633 5370,5922,6112,6700,6902,7526,7740,8400,8626,9322
%N A014633 Even pentagonal numbers.
%H A014633 Vincenzo Librandi, <a href="/A014633/b014633.txt">Table of n, a(n) for n = 0..10000</a>
%H A014633 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A014633 G.f.: 2*(6+5*x+12*x^2+x^3)/((1+x)^2*(1-x)^3). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009, corrected by _R. J. Mathar_, Sep 16 2009
%F A014633 From _Ant King_, Aug 16 2011: (Start)
%F A014633 a(n) = a(n-1) +2*a(n-2) -2*a(n-3) -a(n-4) +a(n-5).
%F A014633 a(n) = 48+2*a(n-2)-a(n-4).
%F A014633 a(n) = 1/8*(1-3*(-1)^(n+1)+12*(n+1))*(1-(-1)^(n+1)+4*(n+1)).(End)
%F A014633 Sum_{n>=1} 1/a(n) = 3*log(3)/2 - (1/sqrt(3)+1/4)*Pi - sqrt(3)*log(2-sqrt(3))/2. - _Amiram Eldar_, Jan 13 2024
%t A014633 LinearRecurrence[{1,2,-2,-1,1},{0,12,22,70,92},40] (* _Harvey P. Dale_, Aug 26 2014 *)
%t A014633 Select[PolygonalNumber[5,Range[0,100]],EvenQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jan 15 2017 *)
%o A014633 (Magma) [1/8*(1-3*(-1)^(n+1)+12*(n+1))*(1-(-1)^(n+1)+4*(n+1)): n in [0..40]]; // _Vincenzo Librandi_, Aug 17 2011
%o A014633 (PARI) lista(nn) = {forstep (n=0, nn, 2, if (ispolygonal(n, 5), print1(n, ", ")););} \\ _Michel Marcus_, Jun 20 2015
%Y A014633 Cf. A000326, A014632.
%K A014633 nonn,easy
%O A014633 0,2
%A A014633 _Mohammad K. Azarian_
%E A014633 More terms from _Patrick De Geest_