A145696 Numbers Y such that 111*Y^2+37 is a square.

7, 4137, 2440823, 1440081433, 849645604647, 501289466660297, 295759935683970583, 174497860764075983673, 102953442090869146396487, 60742356335752032297943657, 35837887284651608186640361143, 21144292755588113078085515130713

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

Example

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

Mathematica

CoefficientList[Series[7 (x + 1)/(x^2 - 590 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 21 2014 *)

Prog

(PARI) Vec(7*x*(x+1)/(x^2-590*x+1) + O(x^20)) \\ Colin Barker, Oct 21 2014
(Magma) I:=[7, 4137]; [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: A024100 A069644 A203679 * A361452 A338250 A103856

Adjacent sequences: A145693 A145694 A145695 * A145697 A145698 A145699

Keyword

easy,nonn

Author

Richard Choulet, Oct 16 2008

Extensions

Editing and more terms from Colin Barker, Oct 21 2014

Status

approved