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A041081 Denominators of continued fraction convergents to sqrt(47). 2
1, 1, 6, 7, 90, 97, 575, 672, 8639, 9311, 55194, 64505, 829254, 893759, 5298049, 6191808, 79599745, 85791553, 508557510, 594349063, 7640746266, 8235095329, 48816222911, 57051318240, 733432041791, 790483360031, 4685848841946, 5476332201977, 70401835265670 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,96,0,0,0,-1).

FORMULA

G.f.: -(x^2-x-1)*(x^4+7*x^2+1) / (x^8-96*x^4+1). - Colin Barker, Nov 12 2013

a(n) = 96*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 11 2013

MATHEMATICA

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[47], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011 *)

CoefficientList[Series[(1 + x + 6 x^2 + 7 x^3 - 6 x^4 + x^5 - x^6)/(x^8 - 96 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)

PROG

(MAGMA) I:=[1, 1, 6, 7, 90, 97, 575, 672]; [n le 8 select I[n] else 96*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

CROSSREFS

Cf. A010501, A041080.

Sequence in context: A232008 A156791 A223532 * A041082 A036417 A267255

Adjacent sequences:  A041078 A041079 A041080 * A041082 A041083 A041084

KEYWORD

nonn,cofr,easy,frac

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 12 2013

STATUS

approved

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Last modified December 11 21:15 EST 2017. Contains 295919 sequences.