A114050 x-values in the solution to x^2 - 22*y^2 = 1.

1, 197, 77617, 30580901, 12048797377, 4747195585637, 1870383011943601, 736926159510193157, 290347036464004160257, 114395995440658128948101, 45071731856582838801391537, 17758147955498197829619317477

Offset: 1

Author

Cino Hilliard, Feb 01 2006

Keywords

• nonn
• easy

Comments

A Pellian equation (Pell's equation). - Benoit Cloitre, Feb 03 2006

The corresponding values of y are in A174766. - Vincenzo Librandi, Dec 21 2011

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Tanya Khovanova, Recursive Sequences
• John Robertson, Home page.
• Index entries for linear recurrences with constant coefficients, signature (394,-1).

Programs

Magma

I:=[1,197]; [n le 2 select I[n] else 394*Self(n-1)-Self(n-2): n in [1..40]]; // Vincenzo Librandi, Dec 21 2011

Mathematica

LinearRecurrence[{394,-1},{1,197},20] (* Harvey P. Dale, Nov 03 2011 *)

PARI

g(n,k=22) = for(y=0,n,x=k*y^2+1;if(issquare(x),print1(sqrtint(x), ", ")))

PARI

a=vector(12); a[1]=1; a[2]=197; for(i=3, #a, a[i]=394*a[i-1]-a[i-2]); a \\ Benoit Cloitre, Feb 03 2006

Formula

a(n) = 394*a(n-1) - a(n-2); a(1)=1, a(2)=197. - Benoit Cloitre, Feb 03 2006

G.f.: x*(1-197*x)/(1 - 394*x + x^2). - Philippe Deléham, Nov 18 2008

Extensions

More terms from Benoit Cloitre, Feb 03 2006

Offset changed from 0 to 1, g.f. and formula adapted by Vincenzo Librandi, Dec 21 2011