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A041283 Denominators of continued fraction convergents to sqrt(154). 2
1, 2, 5, 17, 22, 61, 83, 310, 703, 1716, 41887, 85490, 212867, 724091, 936958, 2598007, 3534965, 13202902, 29940769, 73084440, 1783967329, 3641019098, 9066005525, 30839035673, 39905041198, 110649118069, 150554159267, 562311595870, 1275177351007 (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 (0,0,0,0,0,0,0,0,0,42590,0,0,0,0,0,0,0,0,0,-1).

FORMULA

G.f.: -(x^18 -2*x^17 +5*x^16 -17*x^15 +22*x^14 -61*x^13 +83*x^12 -310*x^11 +703*x^10 -1716*x^9 -703*x^8 -310*x^7 -83*x^6 -61*x^5 -22*x^4 -17*x^3 -5*x^2 -2*x -1) / (x^20 -42590*x^10 +1). - Colin Barker, Nov 14 2013

a(n) = 42590*af(n-10) - a(n-20). - Vincenzo Librandi, Dec 14 2013

MATHEMATICA

Denominator/@Convergents[Sqrt[154], 30] (* Harvey P. Dale, Jul 13 2011 *)

CoefficientList[Series[-(x^18 - 2 x^17 + 5 x^16 - 17 x^15 + 22 x^14 - 61 x^13 + 83 x^12 - 310 x^11 + 703 x^10 - 1716 x^9 - 703 x^8 - 310 x^7 - 83 x^6 - 61 x^5 - 22 x^4 - 17 x^3 - 5 x^2 - 2 x - 1)/(x^20 - 42590 x^10 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 14 2013 *)

PROG

(MAGMA) I:=[1, 2, 5, 17, 22, 61, 83, 310, 703, 1716, 41887, 85490, 212867, 724091, 936958, 2598007, 3534965, 13202902, 29940769, 73084440]; [n le 20 select I[n] else 42590*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 14 2013

CROSSREFS

Cf. A041282, A010205.

Sequence in context: A075612 A156010 A215273 * A042049 A069689 A307479

Adjacent sequences:  A041280 A041281 A041282 * A041284 A041285 A041286

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 September 24 07:01 EDT 2020. Contains 337317 sequences. (Running on oeis4.)