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A169622 a(n) = a(n-1) + Fibonacci(n), a(1)=5.

%I A169622 #28 Sep 08 2022 08:45:49
%S A169622 5,6,8,11,16,24,37,58,92,147,236,380,613,990,1600,2587,4184,6768,
%T A169622 10949,17714,28660,46371,75028,121396,196421,317814,514232,832043,
%U A169622 1346272,2178312,3524581,5702890,9227468,14930355,24157820,39088172,63245989,102334158
%N A169622 a(n) = a(n-1) + Fibonacci(n), a(1)=5.
%H A169622 Vincenzo Librandi, <a href="/A169622/b169622.txt">Table of n, a(n) for n = 1..250</a>
%H A169622 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1).
%F A169622 a(n) = 5 + A168193(n)/2.
%F A169622 a(n) = 2*a(n-1) - a(n-3) = 3 + A000045(n+2). - _R. J. Mathar_ Dec 04 2009
%F A169622 G.f.: x*(-5+4*x+4*x^2) / ((1-x)*(x^2+x-1)). - _R. J. Mathar_ Dec 04 2009
%F A169622 a(n) = 3 + (2^(-1-n)*((1-sqrt(5))^n*(-3+sqrt(5)) + (1+sqrt(5))^n*(3+sqrt(5)))) / sqrt(5). - _Colin Barker_, Apr 20 2017
%e A169622 n=2: a(1)+Fibonacci(2) = 5+1 = 6.
%e A169622 n=3: a(2)+Fibonacci(3) = 6+2 = 8.
%t A169622 RecurrenceTable[{a[1]==5,a[n]==a[n-1]+Fibonacci[n]},a[n],{n,40}] (* or *) LinearRecurrence[{2,0,-1},{5,6,8},40] (* _Harvey P. Dale_, Jul 20 2011 *)
%o A169622 (Magma) [ n eq 1 select 5 else Self(n-1)+Fibonacci(n): n in [1..40] ];  // _Klaus Brockhaus_, Jan 31 2011
%o A169622 (PARI) Vec((5 - 4*x - 4*x^2) / ((1 - x)*(1 - x - x^2)) + O(x^40)) \\ _Colin Barker_, Apr 20 2017
%Y A169622 Cf. A166876, A168193, A000045.
%K A169622 nonn,easy
%O A169622 1,1
%A A169622 _Geoff Ahiakwo_, Dec 03 2009