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%I #17 Feb 12 2024 09:39:26
%S 1,4097,16789505,68803387393,281956264747009,1155456704129855489,
%T 4735061291567883046913,19404280017388480596393985,
%U 79518734776196701916139503617,325867755708574067063859089428481,1335405983375001750630992632338411521
%N Pell equation solutions (32*b(n))^2 - 41*(5*a(n))^2 = -1 with b(n) := A226694(n), n>=0.
%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4098,-1)
%F a(n) = S(n,4098)- S(n-1,4098), n>=0, with the Chebyshev S-polynomials (A049310).
%F O.g.f.: (1-x)/(1 - 4098*x + x^2).
%F a(n) = 4098*a(n-1) - a(n-2), n >= 1, a(-1) = 1, a(0) =1.
%e Pell n=0: 32^2 - 41*5^2 = -1.
%e Pell n=1: (32*4099)^2 - 41*(5*4097)^2 = -1.
%t LinearRecurrence[{4098,-1},{1,4097},20] (* _Harvey P. Dale_, May 17 2015 *)
%Y Cf. A049310, A226694.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Jun 20 2013
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