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Concatenate a(n-2) and a(n-1) to get a(n); start with a(0)=0, a(1)=1, delete the leading zero. Also: concatenate Fibonacci(n) 1's.
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%I #32 Sep 08 2022 08:45:31

%S 0,1,1,11,111,11111,11111111,1111111111111,111111111111111111111,

%T 1111111111111111111111111111111111,

%U 1111111111111111111111111111111111111111111111111111111

%N Concatenate a(n-2) and a(n-1) to get a(n); start with a(0)=0, a(1)=1, delete the leading zero. Also: concatenate Fibonacci(n) 1's.

%C Interpreted as base-2 numbers the result is A063896.

%C This sequence differs from A108047 by the leading a(0) = 0. - _Jason Kimberley_, Dec 15 2012

%H Vincenzo Librandi, <a href="/A131293/b131293.txt">Table of n, a(n) for n = 0..18</a>

%F a(n) = a(n-2)*10^ceiling(log_10(a(n-1))) + a(n-1) for n > 1.

%F a(n) = (10^Fibonacci(n) - 1)/9.

%e a(3)=11, a(4)=111, so a(5) = a(4)*a(3) = 11111.

%p a:= n-> parse(cat(0, 1$combinat[fibonacci](n))):

%p seq(a(n), n=0..11); # _Alois P. Heinz_, Apr 17 2020

%t Join[{0},FromDigits/@(PadLeft[{},#,1]&/@Fibonacci[Range[10]])] (* _Harvey P. Dale_, Aug 28 2011 *)

%o (Magma) [(10^Fibonacci(n)-1)/9: n in [0..10]]; // _Vincenzo Librandi_, Aug 29 2011

%o (Haskell)

%o import Data.Function (on)

%o a131293 n = a131293_list !! n

%o a131293_list = 0 : 1 : map read

%o (zipWith ((++) `on` show) a131293_list $ tail a131293_list)

%o -- _Reinhard Zumkeller_, Oct 05 2015

%Y Cf. A000045, A061107.

%Y Cf. A037842, A108047.

%K nonn,base

%O 0,4

%A _Hieronymus Fischer_, Jun 26 2007