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 A206641 Fibonacci sequence beginning 14, 9. 1

%I

%S 14,9,23,32,55,87,142,229,371,600,971,1571,2542,4113,6655,10768,17423,

%T 28191,45614,73805,119419,193224,312643,505867,818510,1324377,2142887,

%U 3467264,5610151,9077415,14687566,23764981,38452547,62217528,100670075,162887603

%N Fibonacci sequence beginning 14, 9.

%H Vincenzo Librandi, <a href="/A206641/b206641.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature(1,1).

%F a(n) = 14*A000045(n) - 5*A000045(n-2). - _R. J. Mathar_, Feb 18 2012

%F From _Andrew Howroyd_, Aug 28 2018: (Start)

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

%F a(n) = 14*Fibonacci(n) - 5*Fibonacci(n-1).

%F G.f.: x*(14 - 5*x)/(1 - x - x^2).

%F (End)

%t LinearRecurrence[{1,1},{14,9},80]

%o (MAGMA) I:=[14, 9]; [n le 2 select I[n] else Self(n-1)+ Self(n-2): n in [1..40]]; \\ _Vincenzo Librandi_, Feb 18 2012

%o (PARI) Vec((14 - 5*x)/(1 - x - x^2) + O(x^30)) \\ _Andrew Howroyd_, Aug 28 2018

%Y Cf. A000045, A206564, A206605.

%K nonn,easy

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Feb 16 2012

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Last modified July 29 17:41 EDT 2021. Contains 346346 sequences. (Running on oeis4.)