A041877 Denominators of continued fraction convergents to sqrt(460).

1, 2, 9, 29, 38, 105, 1088, 2281, 3369, 12388, 52921, 118230, 5018581, 10155392, 45640149, 147075839, 192715988, 532507815, 5517794138, 11568096091, 17085890229, 62825766778, 268388957341, 599603681460, 25451743578661, 51503090838782, 231464106933789

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, 0, 0, 5071502, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: (1 +2*x +9*x^2 +29*x^3 +38*x^4 +105*x^5 +1088*x^6 +2281*x^7 +3369*x^8 +12388*x^9 +52921*x^10 +118230*x^11 -52921*x^12 +12388*x^13 -3369*x^14 +2281*x^15 -1088*x^16 +105*x^17 -38*x^18 +29*x^19 -9*x^20 +2*x^21 -x^22)/(1 -5071502*x^12 +x^24). - Vincenzo Librandi, Dec 26 2013

a(n) = 5071502*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Dec 26 2013

Mathematica

Denominator[Convergents[Sqrt[460], 30]] (* or *) CoefficientList[Series[(1 + 2 x + 9 x^2 + 29 x^3 + 38 x^4 + 105 x^5 + 1088 x^6 + 2281 x^7 + 3369 x^8 + 12388 x^9 + 52921 x^10 + 118230 x^11 - 52921 x^12 + 12388 x^13 - 3369 x^14 + 2281 x^15 - 1088 x^16 + 105 x^17 - 38 x^18 + 29 x^19 - 9 x^20 + 2 x^21 - x^22)/(1 -5071502 x^12 + x^24), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 26 2013 *)

Prog

(Magma) I:=[1, 2, 9, 29, 38, 105, 1088, 2281, 3369, 12388, 52921, 118230, 5018581, 10155392, 45640149, 147075839, 192715988, 532507815, 5517794138, 11568096091, 17085890229, 62825766778, 268388957341, 599603681460]; [n le 24 select I[n] else 5071502*Self(n-12)-Self(n-24): n in [1..40]]; // Vincenzo Librandi, Dec 26 2013

Crossrefs

Cf. A041876.

Sequence in context: A002747 A110377 A338436 * A090208 A123058 A212272

Adjacent sequences: A041874 A041875 A041876 * A041878 A041879 A041880

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 26 2013

Status

approved