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 A104188 #40 Jul 02 2025 16:02:02
%S A104188 0,12,56,132,240,380,552,756,992,1260,1560,1892,2256,2652,3080,3540,
%T A104188 4032,4556,5112,5700,6320,6972,7656,8372,9120,9900,10712,11556,12432,
%U A104188 13340,14280,15252,16256,17292,18360,19460,20592,21756,22952,24180
%N A104188 a(n) = 4*n*(4*n - 1).
%C A104188 There is a ball-hating monster that lives in a box. You throw 4 numbered balls into the box. He throws 2 balls out. Repeat. Then a(n) gives the number of ordered possibilities the monster has to throw the balls back at each stage (2,1 is different from 1,2).
%H A104188 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A104188 a(n) = (4*n)!/(4*n-2)! for n>0.
%F A104188 a(n) = 32*n + a(n-1) - 20 (with a(0)=0). - _Vincenzo Librandi_, Nov 13 2010
%F A104188 From _Colin Barker_, Jun 25 2012: (Start)
%F A104188 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A104188 G.f.: 4*x*(3+5*x)/(1-x)^3. (End)
%F A104188 Sum_{n>=1} 1/a(n) = 3*log(2)/4 - Pi/8. - _Amiram Eldar_, Jan 03 2022
%F A104188 E.g.f.: 4*exp(x)*x*(3 + 4*x). - _Stefano Spezia_, Nov 29 2024
%e A104188 a(2) = (4*2)!/(4*2-2)! = 8!/6! = 8*7 = 56.
%p A104188 for n from 1 to 100 do printf(`%d,`, (4*n-4)*(4*n-5)) od: # _James Sellers_, Apr 10 2005
%o A104188 (PARI) a(n)=4*n*(4*n-1) \\ _Charles R Greathouse IV_, Jun 16 2017
%Y A104188 Cf. A004767, A008586.
%K A104188 nonn,easy
%O A104188 0,2
%A A104188 Ruppi Rana (ruppi.rana(AT)gmail.com), Mar 12 2005
%E A104188 More terms from _James Sellers_, Apr 10 2005
%E A104188 Simpler definition from _Ralf Stephan_, May 20 2007