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%I #26 Mar 01 2022 01:46:07
%S 3,14,17,31,48,79,127,206,333,539,872,1411,2283,3694,5977,9671,15648,
%T 25319,40967,66286,107253,173539,280792,454331,735123,1189454,1924577,
%U 3114031,5038608,8152639,13191247,21343886,34535133,55879019,90414152,146293171,236707323
%N Fibonacci sequence beginning 3, 14.
%H Colin Barker, <a href="/A022125/b022125.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 G.f.: (3 + 11*x)/(1 - x - x^2). - _Philippe Deléham_, Nov 19 2008
%F a(n) = h*Fibonacci(n+k) + Fibonacci(n+k-h) with h=6, k=2. - _Bruno Berselli_, Feb 20 2017
%F From _Colin Barker_, Feb 20 2017: (Start)
%F a(n) = (2^(-1-n)*((1-sqrt(5))^n*(-25+3*sqrt(5)) + (1+sqrt(5))^n*(25+3*sqrt(5)))) / sqrt(5).
%F a(n) = a(n-1) + a(n-2) for n>1.
%F (End)
%F a(n) = Lucas(n+4) + Lucas(n-3). - _Greg Dresden_ and Kathleen Wilson, Feb 28 2022
%t LinearRecurrence[{1, 1}, {3, 14}, 40] (* _Harvey P. Dale_, Oct 24 2013 *)
%o (PARI) Vec((3 + 11*x) / (1 - x - x^2) + O(x^50)) \\ _Colin Barker_, Feb 20 2017
%Y Cf. A000032, A000045.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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