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 A307169 First class of all proper positive solutions y1(n) = a(n) of the Pell equation x^2 - 7*y^2 = 9. 3

%I

%S 4,65,1036,16511,263140,4193729,66836524,1065190655,16976213956,

%T 270554232641,4311891508300,68719709900159,1095203466894244,

%U 17454535760407745,278177368699629676,4433383363433667071,70655956446239043460,1126061919776391028289,17946334759976017409164

%N First class of all proper positive solutions y1(n) = a(n) of the Pell equation x^2 - 7*y^2 = 9.

%C The corresponding x1 solutions are given in A307168.

%C For details see A307168.

%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 (16,-1).

%F G.f.: x*(4 + x)/(1 - 16*x + x^2).

%F a(n) = -S(n, 16) + 20*S(n-1, 16) for n >= 1, with S(n,16) = A077412(n).

%F a(n) = sqrt((A307168(n)^2 - 9)/7) for n >= 1.

%Y Cf. A077412, A307168.

%K nonn,easy

%O 1,1

%A _Wolfdieter Lang_, Mar 27 2019

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Last modified December 13 08:08 EST 2019. Contains 329968 sequences. (Running on oeis4.)