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 A152760 #32 Dec 27 2024 21:02:27
%S A152760 0,4,36,96,184,300,444,616,816,1044,1300,1584,1896,2236,2604,3000,
%T A152760 3424,3876,4356,4864,5400,5964,6556,7176,7824,8500,9204,9936,10696,
%U A152760 11484,12300,13144,14016,14916,15844,16800,17784,18796,19836,20904,22000,23124
%N A152760 4 times 9-gonal numbers: a(n) = 2*n*(7*n-5).
%C A152760 Sequence found by reading the line from 0, in the direction 0, 4, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. The square spiral is related to the primitive Pythagorean triple [3, 4, 5]. - _Omar E. Pol_, Oct 13 2011
%H A152760 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A152760 a(n) = 14*n^2 - 10*n = 4*A001106(n) = 2*A139268(n).
%F A152760 a(n) = a(n-1) + 28*n - 24 (with a(0)=0). - _Vincenzo Librandi_, Nov 26 2010
%F A152760 From _Colin Barker_, Apr 09 2012: (Start)
%F A152760 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A152760 G.f.: 4*x*(1+6*x)/(1-x)^3. (End)
%F A152760 From _Elmo R. Oliveira_, Dec 27 2024: (Start)
%F A152760 E.g.f.: 2*exp(x)*x*(2 + 7*x).
%F A152760 a(n) = n + A195021(n). (End)
%t A152760 s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,4,8!,28}];lst (* _Vladimir Joseph Stephan Orlovsky_, Apr 02 2009 *)
%t A152760 4*PolygonalNumber[9,Range[0,50]] (* Requires Mathematica version 10 or later *) (* or *) LinearRecurrence[{3,-3,1},{0,4,36},50] (* _Harvey P. Dale_, Aug 26 2019 *)
%o A152760 (PARI) a(n)=2*n*(7*n-5) \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A152760 Cf. A001106, A139268, A152759, A195019, A195020, A195021.
%K A152760 easy,nonn
%O A152760 0,2
%A A152760 _Omar E. Pol_, Dec 14 2008