A174748 x-values in the solution to x^2-33*y^2=1.

1, 23, 1057, 48599, 2234497, 102738263, 4723725601, 217188639383, 9985953686017, 459136680917399, 21110301368514337, 970614726270742103, 44627167107085622401, 2051879072199667888343, 94341810154077637241377, 4337671388015371645214999

Offset

1,2

Comments

The corresponding values of y of this Pell equation are in A174772.

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)=1 and a(2)=23.

G.f.: x*(1-23*x)/(1-46*x+x^2).

a(n+1) = S(n,46) - 23*S(n-1,46), n>=0, with Chebyshev's S-polynomials A049310. - Wolfdieter Lang, Jun 19 2013

a(n) = (-4+23/sqrt(33))*(23+4*sqrt(33))^(-n)*(6072+1057*sqrt(33)+sqrt(33)*(23+4*sqrt(33))^(2*n))/2. - Colin Barker, Jun 10 2016

Mathematica

LinearRecurrence[{46, -1}, {1, 23}, 30]

Prog

(Magma) I:=[1, 23]; [n le 2 select I[n] else 46*Self(n-1)-Self(n-2): n in [1..20]];
(PARI) Vec(x*(1-23*x)/(1-46*x+x^2) + O(x^20)) \\ Colin Barker, Jun 10 2016

Crossrefs

Cf. A174772.

Sequence in context: A167244 A130551 A069479 * A042015 A042012 A128404

Adjacent sequences: A174745 A174746 A174747 * A174749 A174750 A174751

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 13 2010

Status

approved