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A041305 Denominators of continued fraction convergents to sqrt(165). 2
1, 1, 6, 13, 71, 84, 2087, 2171, 12942, 28055, 153217, 181272, 4503745, 4685017, 27928830, 60542677, 330642215, 391184892, 9719079623, 10110264515, 60270402198, 130651068911, 713525746753, 844176815664, 20973769322689, 21817946138353 (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 (0,0,0,0,0,2158,0,0,0,0,0,-1).

FORMULA

G.f.: -(x^10 -x^9 +6*x^8 -13*x^7 +71*x^6 -84*x^5 -71*x^4 -13*x^3 -6*x^2 -x -1) / ((x^4 -13*x^2 +1)*(x^8 +13*x^6 +168*x^4 +13*x^2 +1)). - Colin Barker, Nov 15 2013

a(n) = 2158*a(n-6) - a(n-12). - Vincenzo Librandi, Dec 15 2013

MATHEMATICA

Denominator[Convergents[Sqrt[165], 30]] (* Vincenzo Librandi, Dec 15 2013 *)

PROG

(MAGMA) I:=[1, 1, 6, 13, 71, 84, 2087, 2171, 12942, 28055, 153217, 181272]; [n le 12 select I[n] else 2158*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013

CROSSREFS

Cf. A041304, A010213, A178592.

Sequence in context: A177175 A301605 A119110 * A215755 A144535 A042641

Adjacent sequences:  A041302 A041303 A041304 * A041306 A041307 A041308

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 August 22 05:27 EDT 2019. Contains 326172 sequences. (Running on oeis4.)