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 A122571 #57 Oct 29 2024 03:29:16
%S A122571 1,1,13,181,2521,35113,489061,6811741,94875313,1321442641,18405321661,
%T A122571 256353060613,3570537526921,49731172316281,692665874901013,
%U A122571 9647591076297901,134373609193269601,1871582937629476513,26067787517619401581,363077442309042145621,5057016404808970637113
%N A122571 a(n) = 14*a(n-1) - a(n-2), with a(1) = a(2) = 1.
%C A122571 Essentially the same as A001570: 1 followed by A001570.
%C A122571 Each term is a sum of two consecutive squares, or a(n) = k^2 + (k+1)^2 for some k. Squares of each term are the hex numbers, or centered hexagonal numbers: a(n) = A001570(n-1) for n > 1. - _Alexander Adamchuk_, Apr 14 2008
%D A122571 Henry MacKean and Victor Moll, Elliptic Curves, Cambridge University Press, New York, 1997, page 22.
%H A122571 G. C. Greubel, <a href="/A122571/b122571.txt">Table of n, a(n) for n = 1..870</a>
%H A122571 Gareth Jones and David Singerman, <a href="http://blms.oxfordjournals.org/content/28/6/561.extract">Belyi Functions, Hypermaps and Galois Groups</a>, Bull. London Math. Soc., 28 (1996), 561-590.
%H A122571 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A122571 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-1).
%F A122571 G.f.: x*(1-13*x)/(1-14*x+x^2). - _Philippe Deléham_, Nov 17 2008
%F A122571 a(n+1) = A001570(n). - _Ctibor O. Zizka_, Feb 26 2010
%F A122571 a(n) = (1/4)*sqrt( 2 + (2-sqrt(3))^(4*n-6) + (2+sqrt(3))^(4*n-6) ). - _Gerry Martens_, Jun 03 2015
%F A122571 From _G. C. Greubel_, Oct 29 2024: (Start)
%F A122571 a(n) = (1/4)*( (2 + sqrt(3))^(2*n-3) + (2 - sqrt(3))^(2*n-3) ).
%F A122571 E.g.f.: -13 + exp(7*x)*( 13*cosh(4*sqrt(3)*x) - (15*sqrt(3)/2)*sinh(4*sqrt(3)*x) ). (End)
%t A122571 LinearRecurrence[{14, -1}, {1, 1}, 25] (* _Paolo Xausa_, Jan 29 2024 *)
%o A122571 (Magma) [n le 2 select 1 else 14*Self(n-1) -Self(n-2): n in [1..41]]; // _G. C. Greubel_, Oct 29 2024
%o A122571 (SageMath)
%o A122571 A122571=BinaryRecurrenceSequence(14,-1,1,1)
%o A122571 [A122571(n-1) for n in range(1,41)] # _G. C. Greubel_, Oct 29 2024
%Y A122571 Cf. A001570 (essentially the same).
%K A122571 nonn,easy
%O A122571 1,3
%A A122571 _Roger L. Bagula_, Sep 17 2006
%E A122571 Edited by _N. J. A. Sloane_, Sep 21 2006 and Dec 04 2006
%E A122571 a(19)-a(21) from _Paolo Xausa_, Jan 29 2024