%I #34 Feb 18 2024 02:02:08
%S 1,31,32,63,95,158,253,411,664,1075,1739,2814,4553,7367,11920,19287,
%T 31207,50494,81701,132195,213896,346091,559987,906078,1466065,2372143,
%U 3838208,6210351,10048559,16258910
%N Fibonacci sequence beginning 1, 31.
%H Vincenzo Librandi, <a href="/A022401/b022401.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 a(n) = A118654(5, n).
%F G.f.: (1+30*x)/(1-x-x^2). - _Philippe Deléham_, Nov 20 2008
%F a(n) = (2^(-1-n)*((1-sqrt(5))^n*(-61+sqrt(5)) + (1+sqrt(5))^n*(61+sqrt(5)))) / sqrt(5). - _Colin Barker_, Mar 02 2018
%t CoefficientList[Series[(1 + 30 x)/(1 - x - x^2), {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 30 2014 *)
%t Table[Fibonacci[n + 2] + 29*Fibonacci[n], {n, 0, 50}] (* _G. C. Greubel_, Mar 01 2018 *)
%o (Magma) I:=[1, 31]; [n le 2 select I[n] else Self(n-1)+Self(n-2): n in [1..40]]; // _Vincenzo Librandi_, Oct 30 2014
%o (PARI) for(n=0, 40, print1(fibonacci(n+2) + 29*fibonacci(n), ", ")) \\ _G. C. Greubel_, Mar 01 2018
%K nonn
%O 0,2
%A _N. J. A. Sloane_