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%I #34 Mar 16 2023 12:05:03
%S 110,211,321,532,853,1385,2238,3623,5861,9484,15345,24829,40174,65003,
%T 105177,170180,275357,445537,720894,1166431,1887325,3053756,4941081,
%U 7994837,12935918,20930755,33866673,54797428,88664101,143461529
%N a(n) = a(n-1) + a(n-2), starting with 110, 211.
%H Vincenzo Librandi, <a href="/A120727/b120727.txt">Table of n, a(n) for n = 1..286</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F a(0)=101, a(1)=110, a(n) = a(n-1) + a(n-2).
%F G.f.: (110*x + 101*x^2)/(1 - x - x^2). - _Philippe Deléham_, Nov 20 2008
%t d = 10 M = {{0, 1, 0}, {0, 0, 1}, {1, d, d^2}} v[n_] := Table[Fibonacci[n + i], {i, 0, 2}] w[n_] := M.v[n] Table[w[n][[3]], {n, 0, 50}]
%t Transpose[NestList[Flatten[{Last[#],Total[#]}]&,{110,211},40]][[1]] (* or *) Rest[CoefficientList[Series[(110x+101x^2)/(1-x-x^2),{x,0,41}],x]] (* _Harvey P. Dale_, Mar 27 2011 *)
%t LinearRecurrence[{1,1},{110,211},30] (* _Harvey P. Dale_, Jan 01 2023 *)
%o (Magma) [n le 2 select 101*n+9 else Self(n-1)+Self(n-2): n in [1..30]] // _Bruno Berselli_, Mar 28 2011
%o (PARI) a=vector(99);a[1]=110;a[2]=211;for(i=3,#a,a[i]=a[i-1]+a[i-2]);a \\ _Charles R Greathouse IV_, Jun 05 2011
%Y Cf. A000045.
%K nonn,easy
%O 1,1
%A _Roger L. Bagula_, Aug 19 2006
%E Edited by _N. J. A. Sloane_, Dec 04 2006
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