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A041527 Denominators of continued fraction convergents to sqrt(280). 2
1, 1, 3, 4, 11, 15, 491, 506, 1503, 2009, 5521, 7530, 246481, 254011, 754503, 1008514, 2771531, 3780045, 123732971, 127513016, 378759003, 506272019, 1391303041, 1897575060, 62113704961, 64011280021, 190136265003, 254147545024, 698431355051, 952578900075 (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 (0,0,0,0,0,502,0,0,0,0,0,-1).

FORMULA

a(0)=1, a(1)=1, a(2)=3, a(3)=4, a(4)=11, a(5)=15, a(6)=491, a(7)=506, a(8)=1503, a(9)=2009, a(10)=5521, a(11)=7530, a(n)=502*a(n-6)-a(n-12). - Harvey P. Dale, Aug 13 2012

G.f.: -(x^2-x-1)*(x^8+4*x^6+15*x^4+4*x^2+1) / (x^12-502*x^6+1). - Colin Barker, Nov 18 2013

MATHEMATICA

Denominator[Convergents[Sqrt[280], 30]] (* or *) LinearRecurrence[ {0, 0, 0, 0, 0, 502, 0, 0, 0, 0, 0, -1}, {1, 1, 3, 4, 11, 15, 491, 506, 1503, 2009, 5521, 7530}, 30] (* Harvey P. Dale, Aug 13 2012 *)

CoefficientList[Series[-(x^2 - x - 1) (x^8 + 4 x^6 + 15 x^4 + 4 x^2 + 1)/(x^12 - 502 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 19 2013 *)

PROG

(MAGMA) I:=[1, 1, 3, 4, 11, 15, 491, 506, 1503, 2009, 5521, 7530]; [n le 12 select I[n] else 502*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 19 2013

CROSSREFS

Cf. A041526, A040263.

Sequence in context: A046114 A116654 A041020 * A290493 A266384 A248825

Adjacent sequences:  A041524 A041525 A041526 * A041528 A041529 A041530

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 18 2013

STATUS

approved

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Last modified February 20 22:51 EST 2019. Contains 320362 sequences. (Running on oeis4.)