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A041877 Denominators of continued fraction convergents to sqrt(460). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

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

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Last modified December 3 07:15 EST 2022. Contains 358512 sequences. (Running on oeis4.)