A041327 Denominators of continued fraction convergents to sqrt(177).

1, 3, 10, 23, 194, 411, 1427, 4692, 123419, 374949, 1248266, 2871481, 24220114, 51311709, 178155241, 585777432, 15408368473, 46810882851, 155841017026, 358492916903, 3023784352250, 6406061621403, 22241969216459, 73131969270780, 1923673170256739

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,124846,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -3*x^13 +10*x^12 -23*x^11 +194*x^10 -411*x^9 +1427*x^8 -4692*x^7 -1427*x^6 -411*x^5 -194*x^4 -23*x^3 -10*x^2 -3*x -1) / (x^16 -124846*x^8 +1). - Colin Barker, Nov 15 2013

a(n) = 124846*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 15 2013

Mathematica

Denominator[Convergents[Sqrt[177], 30]] (* Harvey P. Dale, Dec 16 2011 *)
CoefficientList[Series[-(x^14 - 3 x^13 + 10 x^12 - 23 x^11 + 194 x^10 - 411 x^9 + 1427 x^8 - 4692 x^7 - 1427 x^6 - 411 x^5 - 194 x^4 - 23 x^3 - 10 x^2 - 3 x - 1)/(x^16 - 124846 x^8 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 15 2013 *)

Prog

(Magma) I:=[1, 3, 10, 23, 194, 411, 1427, 4692, 123419, 374949, 1248266, 2871481, 24220114, 51311709, 178155241, 585777432]; [n le 16 select I[n] else 124846*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013

Crossrefs

Cf. A041326, A010221.

Sequence in context: A092255 A105861 A228493 * A231116 A272953 A259443

Adjacent sequences: A041324 A041325 A041326 * A041328 A041329 A041330

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 15 2013

Status

approved