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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. 7

%I

%S 0,1,2,4,9,18,37,74,148,297,594,1188,2377,4754,9509,19018,38036,76073,

%T 152146,304293,608586,1217172,2434345,4868690,9737380,19474761,

%U 38949522,77899045,155798090,311596180,623192361,1246384722,2492769444,4985538889,9971077778

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

%C a(n) mod 2 = A003849(n);

%C a(n) = A000225(n+1) - A044432(n).

%H Reinhard Zumkeller, <a href="/A182028/b182028.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = 2*a(n-1) + A003849(n) for n > 0, a(0) = 0.

%e 0 -> 0 -> a(0) = 0,

%e 0,1 -> 01 -> a(1) = 1,

%e 0,1,0 -> 010 -> a(2) = 2,

%e 0,1,0,0 -> 0100 -> a(3) = 4,

%e 0,1,0,0,1 -> 01001 -> a(4) = 9,

%e 0,1,0,0,1,0 -> 010010 -> a(5) = 18,

%e 0,1,0,0,1,0,1 -> 0100101 -> a(6) = 37

%e 0,1,0,0,1,0,1,0 -> 01001010 -> a(7) = 74

%e 0,1,0,0,1,0,1,0,0 -> 010010100 -> a(8) = 148,

%e 0,1,0,0,1,0,1,0,0,1 -> 0100101001 -> a(9) = 297.

%t 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 n = a182028_list !! n

%o a182028_list = scanl1 (\v b -> 2 * v + b) a003849_list

%Y Cf. A003842, A003849, A000225, A044432, A214318.

%K nonn,base

%O 0,3

%A _Reinhard Zumkeller_, Apr 07 2012

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Last modified August 11 05:42 EDT 2020. Contains 336422 sequences. (Running on oeis4.)