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A157364 a(n) = 4802*n^2 - 196*n + 1.

%I A157364 #21 Jul 29 2025 18:47:47
%S A157364 4607,18817,42631,76049,119071,171697,233927,305761,387199,478241,
%T A157364 578887,689137,808991,938449,1077511,1226177,1384447,1552321,1729799,
%U A157364 1916881,2113567,2319857,2535751,2761249,2996351,3241057,3495367
%N A157364 a(n) = 4802*n^2 - 196*n + 1.
%C A157364 The identity (4802*n^2-196*n+1)^2-(49*n^2-2*n)*(686*n-14)^2=1 can be written as a(n)^2-A157362(n)*A157363(n)^2=1.
%H A157364 Vincenzo Librandi, <a href="/A157364/b157364.txt">Table of n, a(n) for n = 1..10000</a>
%H A157364 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5773864&amp;tstart=0">X^2-AY^2=1</a>
%H A157364 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A157364 a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
%F A157364 G.f.: x*(x^2 + 4996*x + 4607)/(1-x)^3.
%F A157364 E.g.f.: (1 + 4606*x + 4802*x^2)*exp(x) - 1. - _G. C. Greubel_, Feb 02 2018
%t A157364 LinearRecurrence[{3,-3,1},{4607,18817,42631},50]
%t A157364 Table[4802n^2-196n+1,{n,30}] (* _Harvey P. Dale_, Jul 29 2021 *)
%o A157364 (Magma) I:=[4607, 18817, 42631]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
%o A157364 (PARI) a(n) = 4802*n^2-196*n+1
%Y A157364 Cf. A157362, A157363.
%K A157364 nonn,easy
%O A157364 1,1
%A A157364 _Vincenzo Librandi_, Feb 28 2009