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A036299 Binary Fibonacci (or rabbit) sequence. 11

%I

%S 1,10,101,10110,10110101,1011010110110,101101011011010110101,

%T 1011010110110101101011011010110110,

%U 1011010110110101101011011010110110101101011011010110101

%N Binary Fibonacci (or rabbit) sequence.

%C A055642(a(n)) = A000045(n+2). - _Reinhard Zumkeller_, Jul 06 2014

%D N. G. De Bruijn, (1989, January). Updown generation of Beatty sequences. Koninklijke Nederlandsche Akademie van Wetenschappen (Indationes Math.), Proc., Ser. A, 92:4 (1968), 385-407. See Fig. 3.

%D J. Kappraff, D. Blackmore and G. Adamson, Phyllotaxis as a dynamical system: a study in number, Chap. 17 of Jean and Barabe, eds., Symmetry in Plants, World Scientific, Studies in Math. Biology and Medicine, Vol. 4.

%H Reinhard Zumkeller, <a href="/A036299/b036299.txt">Table of n, a(n) for n = 0..14</a>

%H M. S. El Naschie, <a href="http://dx.doi.org/10.1016/0898-1221(95)00062-4">Statistical geometry of a Cantor discretum and semiconductors</a>, Computers Math. Applic., 29 (No, 12, 1995), 103-110.

%H C. J. Glasby, S. P. Glasby and F. Pleijel, <a href="http://dx.doi.org/10.1098/rspb.2008.0418">Worms by number</a>, Proc. Roy. Soc. B, Proc. Biol. Sci. 275 (1647) (2008) 2071-2076.

%H H. W. Gould, J. B. Kim and V. E. Hoggatt, Jr., <a href="http://www.fq.math.ca/Scanned/15-4/gould.pdf">Sequences associated with t-ary coding of Fibonacci's rabbits</a>, Fib. Quart., 15 (1977), 311-318.

%F a(n+1) = concatenation of a(n) and a(n-1).

%t nxt[{a_,b_}]:=FromDigits[Join[IntegerDigits[b],IntegerDigits[a]]]; Transpose[NestList[{Last[#],nxt[#]}&,{1,10},10]][[1]] (* _Harvey P. Dale_, Oct 16 2011 *)

%o (Haskell)

%o a036299 n = a036299_list !! n

%o a036299_list = map read rabbits :: [Integer] where

%o rabbits = "1" : "10" : zipWith (++) (tail rabbits) rabbits

%o -- _Reinhard Zumkeller_, Jul 06 2014

%o (Python)

%o def aupton(terms):

%o alst = [1, 10]

%o while len(alst) < terms: alst.append(int(str(alst[-1]) + str(alst[-2])))

%o return alst[:terms]

%o print(aupton(9)) # _Michael S. Branicky_, Jan 10 2021

%Y Cf. A005614, A003849.

%Y Column k=10 of A144287.

%K nonn,easy,nice,base

%O 0,2

%A _N. J. A. Sloane_

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Last modified March 2 11:24 EST 2021. Contains 341746 sequences. (Running on oeis4.)