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%I #32 Mar 04 2022 01:32:35
%S 4,13,17,30,47,77,124,201,325,526,851,1377,2228,3605,5833,9438,15271,
%T 24709,39980,64689,104669,169358,274027,443385,717412,1160797,1878209,
%U 3039006,4917215,7956221,12873436,20829657,33703093,54532750,88235843,142768593
%N Fibonacci sequence beginning 4, 13.
%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 From _Alois P. Heinz_, Jul 31 2008: (Start)
%F G.f.: (4+9*x)/(1-x-x^2).
%F a(n) = term (1,1) in the 1x2 matrix [4,9] . [1,1; 1,0]^n. (End)
%F a(n) = Lucas(n+4) + Fibonacci(n-4). - _Greg Dresden_ and Kyle Wood, Mar 03 2022
%p a:= n -> (Matrix([[4,9]]).Matrix([[1,1],[1,0]])^n)[1,1]:
%p seq(a(n), n=0..35); # _Alois P. Heinz_, Jul 31 2008
%t LinearRecurrence[{1,1},{4,13},40] (* _Harvey P. Dale_, Jul 04 2017 *)
%Y Cf. A000032, A000045.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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