A041480 Numerators of continued fraction convergents to sqrt(257).

16, 513, 16432, 526337, 16859216, 540021249, 17297539184, 554061275137, 17747258343568, 568466328269313, 18208669762961584, 583245898743040001, 18682077429540241616, 598409723644030771713, 19167793234038524936432, 613967793212876828737537

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (32,1).

Crossrefs

Cf. A041481.

Programs

Mathematica

Numerator[Convergents[Sqrt[257],40]] (* or *) LinearRecurrence[{32,1},{16,513},40] (* Harvey P. Dale, Aug 13 2012 *)

Formula

a(n) = 32*a(n-1)+a(n-2), n>1 ; a(0)=16, a(1)=513. G.f.: (16+x)/(1-32*x-x^2). - Philippe Deléham, Nov 23 2008

Extensions

Additional term from Colin Barker, Nov 07 2013