A228580 y-values in the solution to the Pell equation x^2 - 106*y^2 = -1.

389, 24958279289, 1601325744926727089, 102741223129724767598123789, 6591887355607898719696172384139389, 422936165108312951120152699451198782333889, 27135627492838193399902655844465538200645732157289

Offset

1,1

Comments

All terms are multiples of 389.

Links

Colin Barker, Table of n, a(n) for n = 1..120

Index entries for linear recurrences with constant coefficients, signature (64160102,-1).

Formula

a(n) = 64160102*a(n-1)-a(n-2).

G.f.: -389*x*(x-1) / (x^2-64160102*x+1).

Mathematica

LinearRecurrence[{64160102, -1}, {389, 24958279289}, 20] (* or *) With[ {c1= 32080051-3115890Sqrt[106], c2 =32080051+3115890Sqrt[106]}, Table[ (41234c1^n+ 4005Sqrt[106] c1^n+41234c2^n-4005Sqrt[106] c2^n)/212, {n, 10}]]//Simplify (* Harvey P. Dale, Mar 02 2019 *)

Prog

(PARI) Vec(-389*x*(x-1)/(x^2-64160102*x+1) + O(x^30))

Crossrefs

Cf. A228579 gives the corresponding x-values.

Sequence in context: A378695 A299719 A300340 * A242182 A136153 A379532

Adjacent sequences: A228577 A228578 A228579 * A228581 A228582 A228583

Keyword

nonn,easy

Author

Colin Barker, Aug 26 2013

Status

approved