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

1, 3, 6, 9, 13, 18, 25, 35, 50, 73, 109, 166, 257, 403, 638, 1017, 1629, 2618, 4217, 6803, 10986, 17753, 28701, 46414, 75073, 121443, 196470, 317865, 514285, 832098, 1346329, 2178371, 3524642, 5702953, 9227533, 14930422, 24157889, 39088243

Offset

1,2

Comments

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

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Petr Ambroz, Christiane Frougny, Zuzana Masakova and Edita Pelantova, Palindromic complexity of infinite words associated with simple Parry numbers, arXiv:math/0603608 [math.CO], 2006.

Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,1).

Formula

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

G.f.: x*(1-x^2-2*x^3)/((1-x)^2*(1-x-x^2)). - Colin Barker, Nov 08 2012

a(n) = A005843(n-1) + A000045(n). - Gary Detlefs, Dec 31 2012

Maple

with(combinat); seq( 2*(n-1) + fibonacci(n), n=1..45); # G. C. Greubel, Dec 02 2019

Mathematica

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

Prog

(PARI) a(n)=2*n-2+fibonacci(n) \\ Charles R Greathouse IV, Oct 03 2013
(Magma) [2*n-2+Fibonacci(n): n in [1..45]]; // Vincenzo Librandi, Oct 05 2013
(Sage) [2*(n-1) + fibonacci(n) for n in (1..45)] # G. C. Greubel, Dec 02 2019
(GAP) List([1..45], n-> 2*(n-1) + Fibonacci(n) ); # G. C. Greubel, Dec 02 2019

Crossrefs

Cf. A000045, A005843.

Sequence in context: A033436 A059293 A002578 * A307270 A310160 A117469

Adjacent sequences: A129725 A129726 A129727 * A129729 A129730 A129731

Keyword

nonn,easy

Author

Roger L. Bagula, May 12 2007

Extensions

New name from Gary Detlefs, Dec 31 2012

Status

approved