A041525 Denominators of continued fraction convergents to sqrt(279).

1, 1, 3, 7, 10, 27, 64, 91, 2976, 3067, 9110, 21287, 30397, 82081, 194559, 276640, 9047039, 9323679, 27694397, 64712473, 92406870, 249526213, 591459296, 840985509, 27502995584, 28343981093, 84190957770, 196725896633, 280916854403, 758559605439

Offset

0,3

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, 3040, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^14 -x^13 +3*x^12 -7*x^11 +10*x^10 -27*x^9 +64*x^8 -91*x^7 -64*x^6 -27*x^5 -10*x^4 -7*x^3 -3*x^2 -x -1) / (x^16 -3040*x^8 +1). - Colin Barker, Nov 18 2013

a(n) = 3040*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 19 2013

Mathematica

Denominator[Convergents[Sqrt[279], 30]] (* Vincenzo Librandi, Dec 19 2013 *)

Prog

(Magma) I:=[1, 1, 3, 7, 10, 27, 64, 91, 2976, 3067, 9110, 21287, 30397, 82081, 194559, 276640]; [n le 16 select I[n] else 3040*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 19 2013

Crossrefs

Cf. A041524, A040262.

Sequence in context: A235490 A041437 A302279 * A251862 A363651 A056807

Adjacent sequences: A041522 A041523 A041524 * A041526 A041527 A041528

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved