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 A129728 a(n) = 2*n-2 + Fibonacci(n). 1

%I

%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-2 + 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.

%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) - Fibonacci(n-1) + 2

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

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

%t P[1] = 1; P[n_] := P[n] = P[n - 1] + Fibonacci[n] - Fibonacci[n - 1] + 2; Table[P[n], {n, 1, 50}]

%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

%K nonn,easy

%O 1,2

%A _Roger L. Bagula_, May 12 2007

%E New name from _Gary Detlefs_, Dec 31 2012

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Last modified October 16 14:34 EDT 2019. Contains 328095 sequences. (Running on oeis4.)