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Fibonacci sequence beginning 3, 17.
1

%I #24 Feb 21 2017 08:43:01

%S 3,17,20,37,57,94,151,245,396,641,1037,1678,2715,4393,7108,11501,

%T 18609,30110,48719,78829,127548,206377,333925,540302,874227,1414529,

%U 2288756,3703285,5992041,9695326,15687367,25382693,41070060,66452753,107522813,173975566

%N Fibonacci sequence beginning 3, 17.

%H Indranil Ghosh, <a href="/A022127/b022127.txt">Table of n, a(n) for n = 0..4770</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.: (3 + 14*x) / (1 - x - x^2). - _Philippe Deléham_, Nov 19 2008

%F From _Colin Barker_, Feb 21 2017: (Start)

%F a(n) = 2^(-1-n)*((1-sqrt(5))^n*(-31+3*sqrt(5)) + (1+sqrt(5))^n*(31+3*sqrt(5))) / sqrt(5).

%F a(n) = a(n-1) + a(n-2) for n>1.

%F (End)

%t LinearRecurrence[{1,1},{3,17},31] (* or *) CoefficientList[Series[(3+14x)/(1-x-x^2) ,{x,0,30}],x] (* or *) a[0] = 3; a[1] = 17; a[n_]:=a[n-2]+ a[n-1]; Table[a[n],{n,0,30}] (* _Indranil Ghosh_, Feb 20 2017 *)

%o (PARI) Vec((3 + 14*x) / (1 - x - x^2) + O(x^30)) \\ _Colin Barker_, Feb 21 2017

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_