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 A033569 #44 Apr 22 2024 06:34:40
%S A033569 -1,4,21,50,91,144,209,286,375,476,589,714,851,1000,1161,1334,1519,
%T A033569 1716,1925,2146,2379,2624,2881,3150,3431,3724,4029,4346,4675,5016,
%U A033569 5369,5734,6111,6500,6901,7314,7739,8176,8625,9086,9559,10044,10541,11050,11571
%N A033569 a(n) = (2*n - 1)*(3*n + 1).
%C A033569 For n>0, a(n) is the sum of the numbers from 2n+2 to 4n. The last digit of a(n) corresponds to the last digit of the squares mod 10 (A008959). Binomial Transform of a(n) starts: -1, 3, 28, 124, 432, 1328, 3776, 10176, 26368, ... . - _Wesley Ivan Hurt_, Dec 06 2014
%H A033569 Vincenzo Librandi, <a href="/A033569/b033569.txt">Table of n, a(n) for n = 0..1000</a>
%H A033569 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A033569 G.f.: (-1+7*x+6*x^2)/(1-x)^3. - _Vincenzo Librandi_, Jul 07 2012
%F A033569 a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - _Vincenzo Librandi_, Jul 07 2012
%F A033569 E.g.f.: (-1+5*x+6*x^2)*e^x. - _Robert Israel_, Dec 07 2014
%F A033569 a(n) = A060747(n) * A016777(n). - _Reinhard Zumkeller_, Jul 05 2015
%F A033569 Sum_{n>=0} 1/a(n) = 2/5*(log(2)-1) -sqrt(3)*Pi/30 -3*log(3)/10 = -0.6337047... - _R. J. Mathar_, Apr 22 2024
%p A033569 A033569:=n->(2*n-1)*(3*n+1): seq(A033569(n), n=0..50); # _Wesley Ivan Hurt_, Dec 06 2014
%t A033569 CoefficientList[Series[(-1+7*x+6*x^2)/(1-x)^3,{x,0,50}],x] (* _Vincenzo Librandi_, Jul 07 2012 *)
%o A033569 (Magma) [(2*n-1)*(3*n+1): n in [0..50]]; // _Vincenzo Librandi_, Jul 07 2012
%o A033569 (Haskell)
%o A033569 a033569 n = (2 * n - 1) * (3 * n + 1)
%o A033569 a033569_list = map a033569 [0..]
%o A033569 -- _Reinhard Zumkeller_, Jul 05 2015
%o A033569 (PARI) a(n)=(2*n-1)*(3*n+1) \\ _Charles R Greathouse IV_, Jun 17 2017
%o A033569 (Sage) [(2*n-1)*(3*n+1) for n in (0..50)] # _G. C. Greubel_, Apr 02 2019
%o A033569 (GAP) List([0..50], n-> (2*n-1)*(3*n+1)) # _G. C. Greubel_, Apr 02 2019
%Y A033569 Cf. A008959, A060747, A016777, A259758 (subsequence).
%K A033569 sign,easy
%O A033569 0,2
%A A033569 _N. J. A. Sloane_