A041455 Denominators of continued fraction convergents to sqrt(243).

1, 1, 2, 5, 17, 260, 797, 1854, 2651, 4505, 137801, 142306, 280107, 702520, 2387667, 36517525, 111940242, 260398009, 372338251, 632736260, 19354426051, 19987162311, 39341588362, 98670339035, 335352605467, 5128959421040, 15722230868587, 36573421158214

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,140452,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -x^17 +2*x^16 -5*x^15 +17*x^14 -260*x^13 +797*x^12 -1854*x^11 +2651*x^10 -4505*x^9 -2651*x^8 -1854*x^7 -797*x^6 -260*x^5 -17*x^4 -5*x^3 -2*x^2 -x -1) / (x^20 -140452*x^10 +1). - Colin Barker, Nov 18 2013

a(n) = 140452*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 18 2013

Mathematica

Denominator[Convergents[Sqrt[243], 30]] (* Vincenzo Librandi, Dec 18 2013 *)

Prog

(Magma) I:=[1, 1, 2, 5, 17, 260, 797, 1854, 2651, 4505, 137801, 142306, 280107, 702520, 2387667, 36517525, 111940242, 260398009, 372338251, 632736260]; [n le 20 select I[n] else 140452*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 18 2013

Crossrefs

Cf. A041454, A040227.

Sequence in context: A132198 A269835 A111635 * A348927 A081465 A128000

Adjacent sequences: A041452 A041453 A041454 * A041456 A041457 A041458

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved