A042427 Denominators of continued fraction convergents to sqrt(741).

1, 4, 5, 9, 122, 2205, 28787, 30992, 59779, 270108, 14645611, 58852552, 73498163, 132350715, 1794057458, 32425384959, 423324061925, 455749446884, 879073508809, 3972043482120, 215369421543289, 865449729655276, 1080819151198565, 1946268880853841

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,14705390,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -4*x^17 +5*x^16 -9*x^15 +122*x^14 -2205*x^13 +28787*x^12 -30992*x^11 +59779*x^10 -270108*x^9 -59779*x^8 -30992*x^7 -28787*x^6 -2205*x^5 -122*x^4 -9*x^3 -5*x^2 -4*x -1) / (x^20 -14705390*x^10 +1). - Colin Barker, Dec 12 2013

a(n) = 14705390*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Jan 22 2014

Mathematica

Denominator[Convergents[Sqrt[741], 30]] (* Harvey P. Dale, Dec 31 2012 *)
CoefficientList[Series[-(x^18 - 4 x^17 + 5 x^16 - 9 x^15 + 122 x^14 - 2205 x^13 + 28787 x^12 - 30992 x^11 + 59779 x^10 - 270108 x^9 - 59779 x^8 - 30992 x^7 - 28787 x^6 - 2205 x^5 - 122 x^4 - 9 x^3 - 5 x^2 - 4 x - 1)/(x^20 - 14705390 x^10 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 22 2014 *)

Crossrefs

Cf. A042426, A040713.

Sequence in context: A041627 A132811 A042179 * A009778 A215754 A226486

Adjacent sequences: A042424 A042425 A042426 * A042428 A042429 A042430

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 12 2013

Status

approved