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%I #46 Mar 07 2022 02:49:05
%S 3,16,19,35,54,89,143,232,375,607,982,1589,2571,4160,6731,10891,17622,
%T 28513,46135,74648,120783,195431,316214,511645,827859,1339504,2167363,
%U 3506867,5674230,9181097,14855327,24036424,38891751,62928175,101819926,164748101
%N Fibonacci sequence beginning 3, 16.
%C a(n) is the sum of eleven consecutive Fibonacci numbers. a(n) = F(n-6) + F(n-5) + ... + F(n+4), where F(n) = A000045(n), extended so that F(-1) = 1, F(-2) = -1, F(-3) = 2, etc. using the rule F(n-1) = F(n+1) - F(n). - _Graeme McRae_, Apr 24 2014
%H Vincenzo Librandi, <a href="/A022126/b022126.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(0) = 3, a(1) = 16, a(n) = a(n - 2) + a(n - 1).
%F G.f.: (3 + 13x)/(1 - x - x^2). - _Philippe Deléham_, Nov 19 2008
%F From _Colin Barker_, Jun 03 2016: (Start)
%F a(n) = (2^(-1 - n)*((1 - sqrt(5))^n*(-29 + 3*sqrt(5)) + (1 + sqrt(5))^n*(29 + 3*sqrt(5))))/sqrt(5).
%F a(n) = a(n-1) + a(n-2) for n > 1.
%F (End)
%F E.g.f.: (29*sqrt(5)*sinh(sqrt(5)*x/2) + 15*cosh(sqrt(5)*x/2))*exp(x/2)/5. - _Ilya Gutkovskiy_, Jun 03 2016
%F a(n) = Fibonacci(n+6) - Fibonacci(n-5). - _Greg Dresden_, Austen Sharrett, and Aoife Chow, Mar 03 2022
%p seq(coeff(series((3+13*x)/(1-x-x^2),x,n+1), x, n), n = 0 .. 40); # _Muniru A Asiru_, Sep 29 2018
%t CoefficientList[Series[(3 + 13 x)/(1 - x - x^2), {x, 0, 40}], x] (* _Vincenzo Librandi_, Apr 25 2014 *)
%t LinearRecurrence[{1, 1}, {3, 16}, 50] (* _Alonso del Arte_, Sep 29 2018 *)
%o (PARI) Vec((3+13*x)/(1-x-x^2) + O(x^100)) \\ _Colin Barker_, Jun 03 2016
%o (GAP) a:=[3,16];; for n in [3..40] do a[n]:=a[n-1]+a[n-2]; od; a; # _Muniru A Asiru_, Sep 29 2018
%Y Cf. A000045.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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