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A041209 Denominators of continued fraction convergents to sqrt(115). 2
1, 1, 3, 4, 7, 11, 18, 29, 76, 105, 2176, 2281, 6738, 9019, 15757, 24776, 40533, 65309, 171151, 236460, 4900351, 5136811, 15173973, 20310784, 35484757, 55795541, 91280298, 147075839, 385431976, 532507815, 11035588276, 11568096091, 34171780458, 45739876549 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

Index to sequences with linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,2252,0,0,0,0,0,0,0,0,0,-1).

FORMULA

G.f.: -(x^2-x-1)*(x^16+4*x^14+11*x^12+29*x^10+105*x^8+29*x^6+11*x^4+4*x^2+1) / (x^20-2252*x^10+1). - Colin Barker, Nov 14 2013

a(n) = 2252*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 13 2013

MATHEMATICA

Denominator[Convergents[Sqrt[115], 30]] (* Harvey P. Dale, Oct 22 2012 *)

CoefficientList[Series[-(x^2 - x - 1) (x^16 + 4 x^14 + 11 x^12 + 29 x^10 + 105 x^8 + 29 x^6 + 11 x^4 + 4 x^2 + 1)/(x^20 - 2252 x^10 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 13 2013 *)

PROG

(MAGMA) I:=[1, 1, 3, 4, 7, 11, 18, 29, 76, 105, 2176, 2281, 6738, 9019, 15757, 24776, 40533, 65309, 171151, 236460]; [n le 20 select I[n] else 2252*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013

CROSSREFS

Cf. A041208, A010180.

Sequence in context: A075193 A042433 A024319 * A041739 A042593 A041018

Adjacent sequences:  A041206 A041207 A041208 * A041210 A041211 A041212

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 14 2013

STATUS

approved

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Last modified December 22 10:11 EST 2014. Contains 252339 sequences.