A226694 Pell equation solutions (32*a(n))^2 - 41*(5*b(n))^2 = -1 with b(n) := A226695(n), n>=0.

1, 4099, 16797701, 68836974599, 282093905109001, 1156020754299711499, 4737372769026312613901, 19413752451449074792054799, 79557552808665539471527952401, 326026831996158929305246756884499, 1336057877962706483627361738184724501

Offset

0,2

Links

Table of n, a(n) for n=0..10.

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (4098,-1)

Formula

a(n) = S(n,4098)+ S(n-1,4098), n>=0, with the Chebyshev S-polynomials (A049310). 4098 = 17*241 is the smallest positive integer x solution of x^2 - 41*y^2 = +4 with y also positive.

O.g.f.: (1 + x)/(1 - 4098*x + x^2).

a(n) = 4098*a(n-1) - a(n-2), a(-1) = -1 , a(0) = 1.

Example

Pell n=0: 32^2 - 41*5^2 = -1.
Pell n=1: (32*4099)^2 - 41*(5*4097)^2 = -1.

Mathematica

LinearRecurrence[{4098, -1}, {1, 4099}, 20] (* Harvey P. Dale, Sep 23 2017 *)

Crossrefs

Cf. A097314, A097315 (Pell -1 with D = 10), A226695.

Sequence in context: A345605 A346279 A023354 * A345610 A346327 A043476

Adjacent sequences: A226691 A226692 A226693 * A226695 A226696 A226697

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 20 2013

Status

approved