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 A033568 #42 Feb 18 2022 05:16:27
%S A033568 1,2,15,40,77,126,187,260,345,442,551,672,805,950,1107,1276,1457,1650,
%T A033568 1855,2072,2301,2542,2795,3060,3337,3626,3927,4240,4565,4902,5251,
%U A033568 5612,5985,6370,6767,7176,7597,8030,8475,8932,9401,9882,10375,10880,11397,11926
%N A033568 Second pentagonal numbers with odd index: a(n) = (2*n-1)*(3*n-1).
%C A033568 Sequence found by reading the segment (1, 2) together with the line (one of the diagonal axes) from 2, in the direction 2, 15, ..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - _Omar E. Pol_, Sep 08 2011
%H A033568 G. C. Greubel, <a href="/A033568/b033568.txt">Table of n, a(n) for n = 0..1000</a>
%H A033568 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A033568 G.f.: (1-x+12*x^2)/(1-x)^3.
%F A033568 a(n) = a(n-1) + 12*n - 11 (with a(0)=1). - _Vincenzo Librandi_, Nov 17 2010
%F A033568 a(n) = 6*n^2 - 5*n + 1 = A051866(n) + 1. - _Omar E. Pol_, Jul 18 2012
%F A033568 E.g.f.: (1 + x + 6*x^2)*exp(x). - _G. C. Greubel_, Oct 12 2019
%F A033568 From _Amiram Eldar_, Feb 18 2022: (Start)
%F A033568 Sum_{n>=0} 1/a(n) = 1 + Pi/(2*sqrt(3)) + 2*log(2) - 3*log(3)/2.
%F A033568 Sum_{n>=0} (-1)^n/a(n) = 1 + (1/sqrt(3) - 1/2)*Pi - log(2). (End)
%p A033568 seq((2*n-1)*(3*n-1), n=0..50); # _G. C. Greubel_, Oct 12 2019
%t A033568 Table[(2*n-1)*(3*n-1),{n,0,50}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 28 2010 *)
%t A033568 LinearRecurrence[{3,-3,1},{1,2,15},50] (* _Ray Chandler_, Dec 08 2011 *)
%o A033568 (PARI) a(n)=(2*n-1)*(3*n-1) \\ _Charles R Greathouse IV_, Sep 24 2015
%o A033568 (Magma) [(2*n-1)*(3*n-1): n in [0..50]]; // _G. C. Greubel_, Oct 12 2019
%o A033568 (Sage) [(2*n-1)*(3*n-1) for n in range(50)] # _G. C. Greubel_, Oct 12 2019
%o A033568 (GAP) List([0..50], n-> (2*n-1)*(3*n-1)); # _G. C. Greubel_, Oct 12 2019
%Y A033568 Cf. A001318, A005449, A033570, A049452, A049453, A051866.
%K A033568 nonn,easy
%O A033568 0,2
%A A033568 _N. J. A. Sloane_
%E A033568 More terms from _Ray Chandler_, Dec 08 2011