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A041389 Denominators of continued fraction convergents to sqrt(209). 2
1, 2, 11, 35, 81, 278, 1471, 3220, 91631, 186482, 1024041, 3258605, 7541251, 25882358, 136953041, 299788440, 8531029361, 17361847162, 95340265171, 303382642675, 702105550521, 2409699294238, 12750602021711, 27910903337660, 794255895476191, 1616422694290042 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,93102,0,0,0,0,0,0,0,-1).
FORMULA
G.f.: -(x^14 -2*x^13 +11*x^12 -35*x^11 +81*x^10 -278*x^9 +1471*x^8 -3220*x^7 -1471*x^6 -278*x^5 -81*x^4 -35*x^3 -11*x^2 -2*x -1) / (x^16 -93102*x^8 +1). - Colin Barker, Nov 16 2013
a(n) = 93102*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 17 2013
MATHEMATICA
Denominator[Convergents[Sqrt[209], 30]] (* Harvey P. Dale, Nov 07 2012 *)
CoefficientList[Series[-(x^14 - 2 x^13 + 11 x^12 - 35 x^11 + 81 x^10 - 278 x^9 + 1471 x^8 - 3220 x^7 - 1471 x^6 - 278 x^5 - 81 x^4 - 35 x^3 - 11 x^2 - 2 x - 1)/(x^16 - 93102 x^8 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 17 2013 *)
PROG
(Magma) I:=[1, 2, 11, 35, 81, 278, 1471, 3220, 91631, 186482, 1024041, 3258605, 7541251, 25882358, 136953041, 299788440]; [n le 16 select I[n] else 93102*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013
CROSSREFS
Sequence in context: A026946 A204452 A337640 * A205342 A000914 A256317
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 16 2013
STATUS
approved

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Last modified June 23 04:59 EDT 2024. Contains 373629 sequences. (Running on oeis4.)