A145695 Numbers X such that there exists Y in N with X^2=111*Y^2+37.

74, 43586, 25715666, 15172199354, 8951571903194, 5281412250685106, 3116024276332309346, 1838449041623811829034, 1084681818533772646820714, 639960434485884237812392226, 377575571664853166536664592626

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (590,-1).

Formula

a(n+2) = 590*a(n+1)-a(n).

G.f.: -74*x*(x-1) / (x^2-590*x+1). - Colin Barker, Oct 21 2014

Example

a(1)=74 because the first relation is 74^2=111*7^2+37.

Mathematica

CoefficientList[Series[74 (1 - x)/(x^2 - 590 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 21 2014 *)

Prog

(PARI) Vec(-74*x*(x-1)/(x^2-590*x+1) + O(x^20)) \\ Colin Barker, Oct 21 2014
(Magma) I:=[74, 43586]; [n le 2 select I[n] else 590*Self(n-1)-Self(n-2): n in [1..15]]; // Vincenzo Librandi, Oct 21 2014

Crossrefs

Sequence in context: A268090 A278378 A324523 * A116132 A257534 A063680

Adjacent sequences: A145692 A145693 A145694 * A145696 A145697 A145698

Keyword

easy,nonn

Author

Richard Choulet, Oct 16 2008

Extensions

Editing and a(11) from Colin Barker, Oct 21 2014

Status

approved