A174772 y-values in the solution to x^2 - 33*y^2 = 1.

0, 4, 184, 8460, 388976, 17884436, 822295080, 37807689244, 1738331410144, 79925437177380, 3674831778749336, 168962336385292076, 7768592641944686160, 357186299193070271284, 16422801170239287792904, 755091667531814168202300, 34717793905293212449512896

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