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A041815
Denominators of continued fraction convergents to sqrt(428).
2
1, 1, 3, 13, 16, 93, 946, 4823, 5769, 27899, 61567, 89466, 3640207, 3729673, 11099553, 48127885, 59227438, 344265075, 3501878188, 17853656015, 21355534203, 103275792827, 227907119857, 331182912684, 13475223627217, 13806406539901, 41088036707019
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3701774, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: -(x^22 -x^21 +3*x^20 -13*x^19 +16*x^18 -93*x^17 +946*x^16 -4823*x^15 +5769*x^14 -27899*x^13 +61567*x^12 -89466*x^11 -61567*x^10 -27899*x^9 -5769*x^8 -4823*x^7 -946*x^6 -93*x^5 -16*x^4 -13*x^3 -3*x^2 -x -1)/(x^24 -3701774*x^12 +1). - Vincenzo Librandi, Dec 25 2013
a(n) = 3701774*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Dec 25 2013
MATHEMATICA
Denominator[Convergents[Sqrt[428], 30]] (* or *) CoefficientList[Series[-(x^22 - x^21 + 3 x^20 - 13 x^19 + 16 x^18 - 93 x^17 + 946 x^16 - 4823 x^15 + 5769 x^14 - 27899 x^13 + 61567 x^12 - 89466 x^11 - 61567 x^10 - 27899 x^9 - 5769 x^8 - 4823 x^7 - 946 x^6 - 93 x^5 - 16 x^4 - 13 x^3 - 3 x^2 - x - 1)/(x^24 - 3701774 x^12 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 25 2013 *)
PROG
(Magma) I:=[1, 1, 3, 13, 16, 93, 946, 4823, 5769, 27899, 61567, 89466, 3640207, 3729673, 11099553, 48127885, 59227438, 344265075, 3501878188, 17853656015, 21355534203, 103275792827, 227907119857, 331182912684]; [n le 24 select I[n] else 3701774*Self(n-12)-Self(n-24): n in [1..50]]; // Vincenzo Librandi, Dec 25 2013
CROSSREFS
Cf. A041814.
Sequence in context: A022124 A042133 A041297 * A042589 A218364 A370726
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Dec 25 2013
STATUS
approved