A041463 Denominators of continued fraction convergents to sqrt(247).

1, 1, 3, 4, 7, 67, 74, 733, 807, 1540, 3887, 5427, 166697, 172124, 510945, 683069, 1194014, 11429195, 12623209, 125038076, 137661285, 262699361, 663060007, 925759368, 28435841047, 29361600415, 87159041877

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,170584,0,0,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^22 -x^21 +3*x^20 -4*x^19 +7*x^18 -67*x^17 +74*x^16 -733*x^15 +807*x^14 -1540*x^13 +3887*x^12 -5427*x^11 -3887*x^10 -1540*x^9 -807*x^8 -733*x^7 -74*x^6 -67*x^5 -7*x^4 -4*x^3 -3*x^2 -x -1)/(x^24 -170584*x^12 +1). - Vincenzo Librandi, Dec 18 2013

a(n) = 170584*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Dec 18 2013

Mathematica

Denominator[Convergents[Sqrt[247], 30]] (* or *) CoefficientList[Series[-(x^22 - x^21 + 3 x^20 - 4 x^19 + 7 x^18 - 67 x^17 + 74 x^16 - 733 x^15 + 807 x^14 - 1540 x^13 + 3887 x^12 - 5427 x^11 - 3887 x^10 - 1540 x^9 - 807 x^8 - 733 x^7 - 74 x^6 - 67 x^5 - 7 x^4 - 4 x^3 - 3 x^2 - x - 1)/(x^24 - 170584 x^12 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 18 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 170584, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 3, 4, 7, 67, 74, 733, 807, 1540, 3887, 5427, 166697, 172124, 510945, 683069, 1194014, 11429195, 12623209, 125038076, 137661285, 262699361, 663060007, 925759368}, 30] (* Harvey P. Dale, Nov 29 2022 *)

Prog

(Magma) I:=[1, 1, 3, 4, 7, 67, 74, 733, 807, 1540, 3887, 5427, 166697, 172124, 510945, 683069, 1194014, 11429195, 12623209, 125038076, 137661285, 262699361, 663060007, 925759368]; [n le 24 select I[n] else 170584*Self(n-12)-Self(n-24): n in [1..40]]; // Vincenzo Librandi, Dec 18 2013

Crossrefs

Cf. A041462.

Sequence in context: A242859 A134471 A256725 * A041863 A042543 A041987

Adjacent sequences: A041460 A041461 A041462 * A041464 A041465 A041466

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Status

approved