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A041327 Denominators of continued fraction convergents to sqrt(177). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 18 07:19 EDT 2019. Contains 328146 sequences. (Running on oeis4.)