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 A033587 #37 May 04 2021 03:12:09
%S A033587 0,14,44,90,152,230,324,434,560,702,860,1034,1224,1430,1652,1890,2144,
%T A033587 2414,2700,3002,3320,3654,4004,4370,4752,5150,5564,5994,6440,6902,
%U A033587 7380,7874,8384,8910,9452,10010,10584,11174,11780,12402,13040,13694,14364,15050
%N A033587 a(n) = 2*n*(4*n + 3).
%C A033587 The inverse binomial transform is [0, 14, 16, 0, 0, 0, ...]. - _R. J. Mathar_, May 06 2008
%C A033587 Sequence found by reading the line from 0, in the direction 0, 14, ..., in the square spiral whose vertices are the triangular numbers A000217. Opposite numbers to the even hexagonal numbers A014635 in the same spiral. - _Omar E. Pol_, Sep 03 2011
%H A033587 G. C. Greubel, <a href="/A033587/b033587.txt">Table of n, a(n) for n = 0..5000</a>
%H A033587 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A033587 a(n) = 2*A033954(n).
%F A033587 O.g.f.: 2*x*(7+x)/(1-x)^3. - _R. J. Mathar_, May 06 2008
%F A033587 a(n) = 16*n + a(n-1) - 2 with a(0)=0. - _Vincenzo Librandi_, Aug 05 2010
%F A033587 E.g.f.: (8*x^2 + 14*x)*exp(x). - _G. C. Greubel_, Jul 18 2017
%F A033587 From _Vaclav Kotesovec_, Aug 18 2018: (Start)
%F A033587 Sum_{n>=1} 1/a(n) = 2/9 + Pi/12 - log(2)/2.
%F A033587 Sum_{n>=1} (-1)^n/a(n) = 2/9 - Pi/(6*sqrt(2)) - log(2)/6 + log(1+sqrt(2))/(3*sqrt(2)). (End)
%t A033587 Table[2*n(4*n + 3), {n, 0, 100}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 26 2011 *)
%t A033587 LinearRecurrence[{3,-3,1},{0,14,44},80] (* _Harvey P. Dale_, Jun 05 2019 *)
%o A033587 (PARI) a(n)=2*n*(4*n+3) \\ _Charles R Greathouse IV_, Jun 17 2017
%K A033587 nonn,easy
%O A033587 0,2
%A A033587 _N. J. A. Sloane_