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%I #43 Dec 30 2023 23:41:43
%S 0,1,9,83,765,7051,64989,599003,5521005,50887051,469025469,4323003323,
%T 39845080845,367251734251,3384955769949,31199105398043,
%U 287561860122285,2650454951896651,24429218287314429,225163874489623163,2075333306981237325,19128327511810382251
%N Expansion of g.f. x/(1 - 9*x - 2*x^2).
%H Vincenzo Librandi, <a href="/A015579/b015579.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,2).
%F a(n) = 9*a(n-1) + 2*a(n-2).
%F E.g.f.: 2*exp(9*x/2)*sinh(sqrt(89)*x/2)/sqrt(89). - _Stefano Spezia_, Apr 06 2023
%t Join[{a=0,b=1},Table[c=9*b+2*a;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 27 2011 *)
%t LinearRecurrence[{9, 2}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 14 2012 *)
%t CoefficientList[Series[x/(1-9x-2x^2),{x,0,30}],x] (* _Harvey P. Dale_, Aug 14 2023 *)
%o (Sage) [lucas_number1(n,9,-2) for n in range(0, 19)] # _Zerinvary Lajos_, Apr 26 2009
%o (Magma) [n le 2 select n-1 else 9*Self(n-1) + 2*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 14 2012
%o (PARI) x='x+O('x^30); concat([0], Vec(x/(1-9*x-2*x^2))) \\ _G. C. Greubel_, Jan 06 2018
%Y Cf. A099371.
%K nonn,easy
%O 0,3
%A _Olivier Gérard_
%E Extended by _T. D. Noe_, May 23 2011
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