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 A174772 y-values in the solution to x^2 - 33*y^2 = 1. 2
 0, 4, 184, 8460, 388976, 17884436, 822295080, 37807689244, 1738331410144, 79925437177380, 3674831778749336, 168962336385292076, 7768592641944686160, 357186299193070271284, 16422801170239287792904, 755091667531814168202300, 34717793905293212449512896 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The corresponding values of x of this Pell equation are in A174748. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..200 Index entries for linear recurrences with constant coefficients, signature (46,-1). FORMULA a(n) = 46*a(n-1)-a(n-2) with a(1)=0, a(2)=4. G.f.: 4*x^2/(1-46*x+x^2). a(n) = 4*S(n-2,46), n>=1, with Chebyshev's S polynomials A049310 and S(-1,x)=0. - Wolfdieter Lang, Jun 19 2013 a(n) = (-4+23/sqrt(33))*(23+4*sqrt(33))^(-n)*(-1057-184*sqrt(33)+(23+4*sqrt(33))^(2*n))/2. - Colin Barker, Jun 10 2016 EXAMPLE For n=3 a(3)=46*4-0=184; n=4, a(4)=46*184-4=8460. MATHEMATICA LinearRecurrence[{46, -1}, {0, 4}, 30] PROG (Magma) I:=[0, 4]; [n le 2 select I[n] else 46*Self(n-1)-Self(n-2): n in [1..20]]; (PARI) Vec(4*x^2/(1-46*x+x^2) + O(x^20)) \\ Colin Barker, Jun 10 2016 CROSSREFS Cf. A174748. Sequence in context: A322915 A221046 A024266 * A146549 A156905 A202631 Adjacent sequences: A174769 A174770 A174771 * A174773 A174774 A174775 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Apr 14 2010 STATUS approved

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Last modified September 28 03:41 EDT 2023. Contains 365715 sequences. (Running on oeis4.)