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A041859
Denominators of continued fraction convergents to sqrt(451).
2
1, 4, 17, 38, 321, 6779, 54553, 115885, 518093, 2188257, 92424887, 371887805, 1579976107, 3531840019, 29834696259, 630060461458, 5070318387923, 10770697237304, 48153107337139, 203383126585860, 8590244423943259, 34564360822358896, 146847687713378843
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 92942980, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: -(x^18 -4*x^17 +17*x^16 -38*x^15 +321*x^14 -6779*x^13 +54553*x^12 -115885*x^11 +518093*x^10 -2188257*x^9 -518093*x^8 -115885*x^7 -54553*x^6 -6779*x^5 -321*x^4 -38*x^3 -17*x^2 -4*x -1)/(x^20 -92942980*x^10 +1). - Vincenzo Librandi, Dec 26 2013
a(n) = 92942980*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 26 2013
MATHEMATICA
Denominator[Convergents[Sqrt[451], 30]] (* or *) CoefficientList[Series[-(x^18 - 4 x^17 + 17 x^16 - 38 x^15 + 321 x^14 - 6779 x^13 + 54553 x^12 - 115885 x^11 + 518093 x^10 - 2188257 x^9 - 518093 x^8 - 115885 x^7 - 54553 x^6 - 6779 x^5 - 321 x^4 - 38 x^3 - 17 x^2 - 4 x - 1)/(x^20 - 92942980 x^10 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 26 2013 *)
PROG
(Magma) I:=[1, 4, 17, 38, 321, 6779, 54553, 115885, 518093, 2188257, 92424887, 371887805, 1579976107, 3531840019, 29834696259, 630060461458, 5070318387923, 10770697237304, 48153107337139, 203383126585860]; [n le 20 select I[n] else 92942980*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 26 2013
CROSSREFS
Cf. A041858.
Sequence in context: A356347 A182868 A178947 * A022266 A273309 A145995
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Dec 26 2013
STATUS
approved