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A041144 Numerators of continued fraction convergents to sqrt(82). 2

%I

%S 9,163,2943,53137,959409,17322499,312764391,5647081537,101960232057,

%T 1840931258563,33238722886191,600137943210001,10835721700666209,

%U 195643128555201763,3532412035694297943,63779059771052564737,1151555487914640463209,20791777842234580902499

%N Numerators of continued fraction convergents to sqrt(82).

%H Vincenzo Librandi, <a href="/A041144/b041144.txt">Table of n, a(n) for n = 0..200</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (18,1).

%F a(n)=18*a(n-1)+a(n-2), n>1 ; a(0)=9, a(1)=163 . G.f.: (9+x)/(1-18*x-x^2). [From _Philippe Deléham_, Nov 21 2008]

%F a(n)=(9/2)*{[9-sqrt(82)]^n+[9+sqrt(82)]^n}+(1/2)*sqrt(82)*{[9+sqrt(82)]^n-[9-sqrt(82)]^n}, with n>=0 [From _Paolo P. Lava_, Nov 28 2008]

%t CoefficientList[Series[(9 + x)/(1 - 18 x - x^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 29 2013 *)

%Y Cf. A010533, A041145.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 05 2013

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Last modified November 22 00:32 EST 2019. Contains 329383 sequences. (Running on oeis4.)