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%I #24 Nov 03 2024 02:13:04
%S 0,1,1523,2319528,3532639621,5380207823255,8194052982177744,
%T 12479537311648880857,19006327131588263367467,
%U 28946623741871613459771384,44085688952543335710968450365,67142475328099758416191490134511
%N Solutions y/(3*5*13) of the Pell equation x^2 - 61*y^2 = +4.
%C y' = a(n) and x = b(n) := A226699(n) are the nonnegative solutions of x^2 - 61*(3*5*13*y')^2 = +4. This is x^2 - D*y'^2 = +4 with D = 61*(3*5*13)^2 = 61*195^2 = 2319525.
%D T. Nagell, Introduction to Number Theory, Chelsea Publishing Company, New York, 1964, ch. Vi, 58., p. 204-212.
%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 (1523,-1).
%F a(n) = S(n-1,1523), n >= 0, with the Chebyshev S-polynomials (A049310), with S(-1, 0) = 0.
%F O.g.f. x/(1- 1523*x + x^2).
%F a(n) = 1523*a(n-1) - a(n-2), n >= 1, a(-1) = -1, a(0) = 0.
%t LinearRecurrence[{1523,-1},{0,1},20] (* _Harvey P. Dale_, Apr 24 2023 *)
%Y Cf. A226699.
%K nonn,easy
%O 0,3
%A _Wolfdieter Lang_, Jun 27 2013