A042807 Denominators of continued fraction convergents to sqrt(934).

1, 1, 2, 7, 9, 16, 57, 1726, 5235, 6961, 12196, 43549, 55745, 99294, 6013385, 6112679, 12126064, 42490871, 54616935, 97107806, 345940353, 10475318396, 31771895541, 42247213937, 74019109478, 264304542371, 338323651849, 602628194220, 36496015305049

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, 0, 0, 6069130, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^26 -x^25 +2*x^24 -7*x^23 +9*x^22 -16*x^21 +57*x^20 -1726*x^19 +5235*x^18 -6961*x^17 +12196*x^16 -43549*x^15 +55745*x^14 -99294*x^13 -55745*x^12 -43549*x^11 -12196*x^10 -6961*x^9 -5235*x^8 -1726*x^7 -57*x^6 -16*x^5 -9*x^4 -7*x^3 -2*x^2 -x -1)/(x^28 -6069130*x^14 +1). - Vincenzo Librandi, Jan 30 2014

a(n) = 6069130*a(n-14) - a(n-28) for n>27. - Vincenzo Librandi, Jan 30 2014

Mathematica

Denominator[Convergents[Sqrt[934], 30]] (* Harvey P. Dale, May 28 2013 *)
CoefficientList[Series[-(x^26 - x^25 + 2 x^24 - 7 x^23 + 9 x^22 - 16 x^21 + 57 x^20 - 1726 x^19 + 5235 x^18 - 6961 x^17 + 12196 x^16 - 43549 x^15 + 55745 x^14 - 99294 x^13 - 55745 x^12 - 43549 x^11 - 12196 x^10 - 6961 x^9 - 5235 x^8 - 1726 x^7 - 57 x^6 - 16 x^5 - 9 x^4 - 7 x^3 - 2 x^2 - x - 1)/(x^28 - 6069130 x^14 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 30 2014 *)

Crossrefs

Cf. A042806, A040903.

Sequence in context: A041395 A042345 A041973 * A005988 A199537 A079326

Adjacent sequences: A042804 A042805 A042806 * A042808 A042809 A042810

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Jan 20 2014

Status

approved