A041485 Denominators of continued fraction convergents to sqrt(259).

1, 10, 11, 32, 107, 460, 1487, 3434, 4921, 52644, 1689529, 16947934, 18637463, 54222860, 181306043, 779447032, 2519647139, 5818741310, 8338388449, 89202625800, 2862822414049, 28717426766290, 31580249180339, 91877925126968, 307214024561243, 1320734023371940

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 1694450, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^18 -10*x^17 +11*x^16 -32*x^15 +107*x^14 -460*x^13 +1487*x^12 -3434*x^11 +4921*x^10 -52644*x^9 -4921*x^8 -3434*x^7 -1487*x^6 -460*x^5 -107*x^4 -32*x^3 -11*x^2 -10*x -1) / (x^20 -1694450*x^10 +1). - Colin Barker, Nov 18 2013

a(n) = 1694450*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 18 2013

Mathematica

Denominator[Convergents[Sqrt[259], 30]] (* Vincenzo Librandi, Dec 18 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 1694450, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 10, 11, 32, 107, 460, 1487, 3434, 4921, 52644, 1689529, 16947934, 18637463, 54222860, 181306043, 779447032, 2519647139, 5818741310, 8338388449, 89202625800}, 40] (* Harvey P. Dale, Aug 03 2021 *)

Prog

(Magma) I:=[1, 10, 11, 32, 107, 460, 1487, 3434, 4921, 52644, 1689529, 16947934, 18637463, 54222860, 181306043, 779447032, 2519647139, 5818741310, 8338388449, 89202625800]; [n le 20 select I[n] else 1694450*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 18 2013

Crossrefs

Cf. A041484, A040242.

Sequence in context: A108580 A356279 A041208 * A041206 A339078 A097990

Adjacent sequences: A041482 A041483 A041484 * A041486 A041487 A041488

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved