A041905 Denominators of continued fraction convergents to sqrt(474).

1, 1, 4, 9, 13, 22, 35, 232, 267, 499, 766, 2031, 6859, 8890, 380239, 389129, 1547626, 3484381, 5032007, 8516388, 13548395, 89806758, 103355153, 193161911, 296517064, 786196039, 2655105181, 3441301220, 147189756421, 150631057641, 599082929344

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, 387098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^26 -x^25 +4*x^24 -9*x^23 +13*x^22 -22*x^21 +35*x^20 -232*x^19 +267*x^18 -499*x^17 +766*x^16 -2031*x^15 +6859*x^14 -8890*x^13 -6859*x^12 -2031*x^11 -766*x^10 -499*x^9 -267*x^8 -232*x^7 -35*x^6 -22*x^5 -13*x^4 -9*x^3 -4*x^2 -x -1)/(x^28 -387098*x^14 +1). - Vincenzo Librandi, Dec 26 2013

a(n) = 387098*a(n-14) - a(n-28) for n>27. - Vincenzo Librandi, Dec 26 2013

Mathematica

Denominator[Convergents[Sqrt[474], 30]] (* or *) CoefficientList[Series[-(x^26 - x^25 + 4 * x^24 - 9 * x^23 + 13 * x^22 - 22 * x^21 + 35 * x^20 - 232 * x^19 + 267 * x^18 - 499 * x^17 + 766 * x^16 - 2031 * x^15 + 6859 * x^14 - 8890 * x^13 - 6859 * x^12 - 2031 * x^11 - 766 * x^10 - 499 * x^9 - 267 * x^8 - 232 * x^7 - 35 * x^6 - 22 * x^5 - 13 * x^4 - 9 * x^3 - 4 * x^2 - x - 1)/(x^28 - 387098 * x^14 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 26 2013 *)

Prog

(Magma) I:=[1, 1, 4, 9, 13, 22, 35, 232, 267, 499, 766, 2031, 6859, 8890, 380239, 389129, 1547626, 3484381, 5032007, 8516388, 13548395, 89806758, 103355153, 193161911, 296517064, 786196039, 2655105181, 3441301220]; [n le 28 select I[n] else 387098*Self(n-14)-Self(n-28): n in [1..50]]; // Vincenzo Librandi, Dec 26 2013

Crossrefs

Cf. A041904.

Sequence in context: A345743 A022130 A042125 * A098004 A257337 A056227

Adjacent sequences: A041902 A041903 A041904 * A041906 A041907 A041908

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 26 2013

Status

approved