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A157363 a(n) = 686*n - 14.

%I A157363 #27 Jul 29 2025 18:47:35
%S A157363 672,1358,2044,2730,3416,4102,4788,5474,6160,6846,7532,8218,8904,9590,
%T A157363 10276,10962,11648,12334,13020,13706,14392,15078,15764,16450,17136,
%U A157363 17822,18508,19194,19880,20566,21252,21938,22624,23310,23996,24682
%N A157363 a(n) = 686*n - 14.
%C A157363 The identity (4802*n^2-196*n+1)^2-(49*n^2-2*n)*(686*n-14)^2=1 can be written as A157364(n)^2-A157362(n)*a(n)^2=1.
%H A157363 Vincenzo Librandi, <a href="/A157363/b157363.txt">Table of n, a(n) for n = 1..10000</a>
%H A157363 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5773864&amp;tstart=0">X^2-AY^2=1</a>
%H A157363 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A157363 a(n) = 2*a(n-1) -a(n-2).
%F A157363 G.f.: 14*x*(48+x)/(1-x)^2.
%F A157363 E.g.f.: 14*(1 - (1-49*x)*exp(x)). - _G. C. Greubel_, Feb 02 2018
%t A157363 LinearRecurrence[{2,-1},{672,1358},50]
%o A157363 (Magma) I:=[672, 1358]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];
%o A157363 (PARI) a(n) = 686*n-14
%Y A157363 Cf. A157362, A157364.
%K A157363 nonn,easy
%O A157363 1,1
%A A157363 _Vincenzo Librandi_, Feb 28 2009