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 A044432 a(n) is the number whose base-2 representation is d(0)d(1)...d(n), where d=A005614 (the infinite Fibonacci word). 4
 1, 2, 5, 11, 22, 45, 90, 181, 363, 726, 1453, 2907, 5814, 11629, 23258, 46517, 93035, 186070, 372141, 744282, 1488565, 2977131, 5954262, 11908525, 23817051, 47634102, 95268205, 190536410, 381072821 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) can also be calculated as floor(2^n * R), where the rabbit constant R=0.709803442861291314641787399444575597012... converges rapidly using the result from Davison described in the comments at A014565. - Federico Provvedi, Oct 24 2018 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..1000 FORMULA a(n) = A000225(n+1) - A182028(n). - Reinhard Zumkeller, Apr 07 2012 a(n) = 2*a(n-1) + A005614(n) for n > 0, a(0) = 1. - Reinhard Zumkeller, Apr 07 2012 From Federico Provvedi, Oct 24 2018: (Start) a(n) = A000079(n) * Sum_{k=0..n} ((floor(phi*(k+1)) - floor(phi*k) - 1)/2^k). a(n) = floor(2^n*(1-Sum_{n >= 1}(-1)^(n+1)*(1+2^Fibonacci(3*n+1))/((2^(Fibonacci(3*n-1))-1)*(2^(Fibonacci(3*n + 2))-1))). a(n) = floor(2^n*R), where R is the rabbit constant. a(n) = floor(2^n/[1, 2, 2, 4, 8, 32, ..., 2^Fibonacci(3*h)]), with h=1 for n=0, h=floor(2+log((n+1)/11)/arcsinh(2)) for n>0. (End) MATHEMATICA FromDigits[(Floor[GoldenRatio(#+1)]-Floor[GoldenRatio #]-1)&@Range@#, 2]&/@Range@40 (* Federico Provvedi, Oct 19 2018 *) Floor[2^#/FromContinuedFraction[2^Fibonacci[Range[0, 3*Max[1, Floor[2+Log[(#+1)/11]/ArcSinh[2]]]]]]]&/@Range[200] (* Federico Provvedi, Nov 01 2018 *) PROG (Haskell) a044432 n = a044432_list !! n a044432_list = scanl1 (\v b -> 2 * v + b) a005614_list -- Reinhard Zumkeller, Apr 07 2012 CROSSREFS Cf. A000225, A005614, A182028, A000079, A014565. Sequence in context: A293362 A084188 A266721 * A033120 A091617 A205880 Adjacent sequences:  A044429 A044430 A044431 * A044433 A044434 A044435 KEYWORD nonn,base AUTHOR EXTENSIONS Offset fixed by Reinhard Zumkeller, Apr 07 2012 STATUS approved

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Last modified August 13 02:52 EDT 2020. Contains 336441 sequences. (Running on oeis4.)