A145694 Numbers Y such that 57*Y^2+19 is a square.

5, 1515, 457525, 138171035, 41727195045, 12601474732555, 3805603642036565, 1149279698420310075, 347078663319291606085, 104816607042727644727595, 31654268248240429416127605, 9559484194361566956025809115, 2886932572428944980290378225125

Offset: 1

Author

Richard Choulet, Oct 16 2008

Keywords

• easy
• nonn

Examples

			a(1)=5 because the first relation is 38^2=57*5^2+19.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (302,-1).

Crossrefs

Cf. A145120.

Programs

Magma

I:=[5, 1515]; [n le 2 select I[n] else 302*Self(n-1)-Self(n-2): n in [1..15]]; // Vincenzo Librandi, Oct 21 2014

Mathematica

CoefficientList[Series[5 (x + 1)/(x^2 - 302 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 21 2014 *)
LinearRecurrence[{302,-1},{5,1515},15] (* Harvey P. Dale, Jun 25 2021 *)

PARI

Vec(5*x*(x+1)/(x^2-302*x+1) + O(x^20)) \\ Colin Barker, Oct 21 2014

Formula

a(n+2) = 302*a(n+1)-a(n).

G.f.: 5*x*(x+1) / (x^2-302*x+1). - Colin Barker, Oct 21 2014

Extensions

Editing and more terms from Colin Barker, Oct 21 2014