A041385 Denominators of continued fraction convergents to sqrt(207).

1, 2, 3, 5, 13, 18, 31, 80, 2271, 4622, 6893, 11515, 29923, 41438, 71361, 184160, 5227841, 10639842, 15867683, 26507525, 68882733, 95390258, 164272991, 423936240, 12034487711, 24492911662, 36527399373, 61020311035, 158568021443, 219588332478

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,2302,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -2*x^13 +3*x^12 -5*x^11 +13*x^10 -18*x^9 +31*x^8 -80*x^7 -31*x^6 -18*x^5 -13*x^4 -5*x^3 -3*x^2 -2*x -1) / ((x^8 -48*x^4 +1)*(x^8 +48*x^4 +1)). - Colin Barker, Nov 16 2013

a(n) = 2302*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 16 2013

Mathematica

Denominator[Convergents[Sqrt[207], 40]] (* Harvey P. Dale, May 03 2012 *)
CoefficientList[Series[-(x^14 - 2 x^13 + 3 x^12 - 5 x^11 + 13 x^10 - 18 x^9 + 31 x^8 - 80 x^7 - 31 x^6 - 18 x^5 - 13 x^4 - 5 x^3 - 3 x^2 - 2 x - 1)/((x^8 - 48 x^4 + 1) (x^8 + 48 x^4 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 16 2013 *)

Prog

(Magma) I:=[1, 2, 3, 5, 13, 18, 31, 80, 2271, 4622, 6893, 11515, 29923, 41438, 71361, 184160]; [n le 16 select I[n] else 2302*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 16 2013

Crossrefs

Cf. A041384, A040192.

Sequence in context: A042261 A112596 A179238 * A108282 A042047 A273939

Adjacent sequences: A041382 A041383 A041384 * A041386 A041387 A041388

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 16 2013

Status

approved