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A041142 Numerators of continued fraction convergents to sqrt(80). 2
8, 9, 152, 161, 2728, 2889, 48952, 51841, 878408, 930249, 15762392, 16692641, 282844648, 299537289, 5075441272, 5374978561, 91075098248, 96450076809, 1634276327192, 1730726404001, 29325898791208, 31056625195209, 526231901914552, 557288527109761 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..199

Index entries for linear recurrences with constant coefficients, signature (0,18,0,-1).

FORMULA

G.f.: (8+9*x+8*x^2-x^3)/(1-18*x^2+x^4).

a(n) = 18*a(n-2) - a(n-4).

a(n) = (-3*(-2-sqrt(5))^(n+1) + 5*(2-sqrt(5))^(n+1) - 3*(-2+sqrt(5))^(n+1) + 5*(2+sqrt(5))^(n+1))/4. - Colin Barker, Mar 27 2016

a(n) = (5 - 3*(-1)^(n+1))*Lucas(3*(n+1))/4. - Ehren Metcalfe, Apr 15 2019

MATHEMATICA

CoefficientList[Series[(8+9*x+8*x^2-x^3)/(1-18*x^2+x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 29 2013 *)

PROG

(PARI) Vec((8+9*x+8*x^2-x^3)/(1-18*x^2+x^4) + O(x^30)) \\ Colin Barker, Mar 27 2016

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (8+9*x+8*x^2-x^3)/(1-18*x^2+x^4) )); // G. C. Greubel, Apr 16 2019

(Sage) ((8+9*x+8*x^2-x^3)/(1-18*x^2+x^4)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Apr 16 2019

CROSSREFS

Cf. A010532, A041143.

Sequence in context: A165467 A239584 A041141 * A307947 A175849 A294468

Adjacent sequences:  A041139 A041140 A041141 * A041143 A041144 A041145

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Colin Barker, Nov 05 2013

First term 1 removed in b-file, formulas and programs by Georg Fischer, Jul 01 2019

STATUS

approved

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Last modified November 19 16:37 EST 2019. Contains 329323 sequences. (Running on oeis4.)