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A182028 Take first n bits of the infinite Fibonacci word A003849, regard them as a binary number, then convert it to base 10.

%I A182028 #17 Feb 13 2016 10:43:24
%S A182028 0,1,2,4,9,18,37,74,148,297,594,1188,2377,4754,9509,19018,38036,76073,
%T A182028 152146,304293,608586,1217172,2434345,4868690,9737380,19474761,
%U A182028 38949522,77899045,155798090,311596180,623192361,1246384722,2492769444,4985538889,9971077778
%N A182028 Take first n bits of the infinite Fibonacci word A003849, regard them as a binary number, then convert it to base 10.
%C A182028 a(n) mod 2 = A003849(n);
%C A182028 a(n) = A000225(n+1) - A044432(n).
%H A182028 Reinhard Zumkeller, <a href="/A182028/b182028.txt">Table of n, a(n) for n = 0..1000</a>
%F A182028 a(n) = 2*a(n-1) + A003849(n) for n > 0, a(0) = 0.
%e A182028 0 ->                            0 -> a(0) = 0,
%e A182028 0,1 ->                         01 -> a(1) = 1,
%e A182028 0,1,0 ->                      010 -> a(2) = 2,
%e A182028 0,1,0,0 ->                   0100 -> a(3) = 4,
%e A182028 0,1,0,0,1 ->                01001 -> a(4) = 9,
%e A182028 0,1,0,0,1,0 ->             010010 -> a(5) = 18,
%e A182028 0,1,0,0,1,0,1 ->          0100101 -> a(6) = 37
%e A182028 0,1,0,0,1,0,1,0 ->       01001010 -> a(7) = 74
%e A182028 0,1,0,0,1,0,1,0,0 ->    010010100 -> a(8) = 148,
%e A182028 0,1,0,0,1,0,1,0,0,1 -> 0100101001 -> a(9) = 297.
%t A182028 nesting = 7; A003849 = Flatten[Nest[{#, #[[1]]}&, {0, 1}, nesting]]; a[n_] := FromDigits[Take[A003849, n+1], 2]; Table[a[n], {n, 0, Length[A003849] - 1}] (* _Jean-François Alcover_, Feb 13 2016 *)
%o A182028 (Haskell)
%o A182028 a182028 n = a182028_list !! n
%o A182028 a182028_list = scanl1 (\v b -> 2 * v + b) a003849_list
%Y A182028 Cf. A003842, A003849, A000225, A044432, A214318.
%K A182028 nonn,base
%O A182028 0,3
%A A182028 _Reinhard Zumkeller_, Apr 07 2012