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A097657 Fibonacci sequence with first two terms 11 and 23. 3

%I #14 Feb 20 2017 10:33:12

%S 11,23,34,57,91,148,239,387,626,1013,1639,2652,4291,6943,11234,18177,

%T 29411,47588,76999,124587,201586,326173,527759,853932,1381691,2235623,

%U 3617314,5852937,9470251,15323188,24793439

%N Fibonacci sequence with first two terms 11 and 23.

%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) = a(n-1) + a(n-2) for n > 1, a(0) = 11, a(1) = 23.

%F G.f.: (11 + 12*x)/(1 - x - x^2). - _Philippe Deléham_, Nov 20 2008

%F a(n) = h*Fibonacci(n+k) + Fibonacci(n+k-h) with h=7, k=3. - _Bruno Berselli_, Feb 20 2017

%t a[0] := 11; a[1] := 23; a[n_] := a[n - 1] + a[n - 2]; Table[a[n], {n, 0, 25}] (* _Stefan Steinerberger_, Mar 06 2006 *)

%o (PARI) a(n)=([0,1; 1,1]^n*[11;23])[1,1] \\ _Charles R Greathouse IV_, Feb 20 2017

%Y Cf. A000045.

%K nonn,easy

%O 0,1

%A _Parthasarathy Nambi_, Sep 20 2004

%E More terms from _Stefan Steinerberger_, Mar 06 2006

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Last modified May 9 10:58 EDT 2024. Contains 372350 sequences. (Running on oeis4.)