%I #47 Sep 08 2022 08:44:45
%S 2,9,11,20,31,51,82,133,215,348,563,911,1474,2385,3859,6244,10103,
%T 16347,26450,42797,69247,112044,181291,293335,474626,767961,1242587,
%U 2010548,3253135,5263683,8516818,13780501,22297319,36077820,58375139,94452959,152828098
%N Fibonacci sequence beginning 2 9.
%H Ivan Panchenko, <a href="/A022114/b022114.txt">Table of n, a(n) for n = 0..1000</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 G.f.: (2+7*x)/(1-x-x^2). - _Wesley Ivan Hurt_, Jun 15 2014
%F a(n) = 10*F(n) + F(n-3). - _J. M. Bergot_, Jul 17 2017
%F a(n) = Fibonacci(n+5) - Lucas(n-2). - _Greg Dresden_ and Christina Savory, Mar 01 2022
%t LinearRecurrence[{1,1},{2,9},40] (* _Harvey P. Dale_, Jul 16 2012 *)
%t CoefficientList[Series[(2 + 7 x)/(1 - x - x^2), {x, 0, 40}], x] (* _Wesley Ivan Hurt_, Jun 15 2014 *)
%o (Magma) a0:=2; a1:=9; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..40]]; // _Bruno Berselli_, Feb 12 2013
%Y Cf. A000032, A000045.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, Jun 14 1998