A041815 Denominators of continued fraction convergents to sqrt(428).

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

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, 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

Adjacent sequences: A041812 A041813 A041814 * A041816 A041817 A041818

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 25 2013

Status

approved