A129728 - OEIS

%I #31 Sep 08 2022 08:45:30

%S 1,3,6,9,13,18,25,35,50,73,109,166,257,403,638,1017,1629,2618,4217,

%T 6803,10986,17753,28701,46414,75073,121443,196470,317865,514285,

%U 832098,1346329,2178371,3524642,5702953,9227533,14930422,24157889,39088243

%N a(n) = 2*(n-1) + Fibonacci(n).

%C Old name was: A palindromic complexity sequence based on the Fibonacci numbers.

%C a(1)=1 gives more primes than a(1)=2 for some reason.

%H Vincenzo Librandi, <a href="/A129728/b129728.txt">Table of n, a(n) for n = 1..1000</a>

%H Petr Ambroz, Christiane Frougny, Zuzana Masakova and Edita Pelantova, <a href="http://arxiv.org/abs/math/0603608">Palindromic complexity of infinite words associated with simple Parry numbers</a>, arXiv:math/0603608 [math.CO], 2006.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-1,1).

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

%F G.f.: x*(1-x^2-2*x^3)/((1-x)^2*(1-x-x^2)). - _Colin Barker_, Nov 08 2012

%F a(n) = A005843(n-1) + A000045(n). - _Gary Detlefs_, Dec 31 2012

%p with(combinat); seq( 2*(n-1) + fibonacci(n), n=1..45); # _G. C. Greubel_, Dec 02 2019

%t a[n_]:= a[n]= If[n==1, 1, a[n-1] + Fibonacci[n-2] +2]; Table[a[n], {n,45}]

%o (PARI) a(n)=2*n-2+fibonacci(n) \\ _Charles R Greathouse IV_, Oct 03 2013

%o (Magma) [2*n-2+Fibonacci(n): n in [1..45]]; // _Vincenzo Librandi_, Oct 05 2013

%o (Sage) [2*(n-1) + fibonacci(n) for n in (1..45)] # _G. C. Greubel_, Dec 02 2019

%o (GAP) List([1..45], n-> 2*(n-1) + Fibonacci(n) ); # _G. C. Greubel_, Dec 02 2019

%Y Cf. A000045, A005843.

%K nonn,easy

%O 1,2

%A _Roger L. Bagula_, May 12 2007

%E New name from _Gary Detlefs_, Dec 31 2012