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A036299
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Binary Fibonacci (or rabbit) sequence.
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11
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OFFSET
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0,2
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COMMENTS
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A055642(a(n)) = A000045(n+2). - Reinhard Zumkeller, Jul 06 2014
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REFERENCES
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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.
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.
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 0..14
M. S. El Naschie, Statistical geometry of a Cantor discretum and semiconductors, Computers Math. Applic., 29 (No, 12, 1995), 103-110.
C. J. Glasby, S. P. Glasby and F. Pleijel, Worms by number, Proc. Roy. Soc. B, Proc. Biol. Sci. 275 (1647) (2008) 2071-2076.
H. W. Gould, J. B. Kim and V. E. Hoggatt, Jr., Sequences associated with t-ary coding of Fibonacci's rabbits, Fib. Quart., 15 (1977), 311-318.
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FORMULA
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a(n+1) = concatenation of a(n) and a(n-1).
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MATHEMATICA
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nxt[{a_, b_}]:=FromDigits[Join[IntegerDigits[b], IntegerDigits[a]]]; Transpose[NestList[{Last[#], nxt[#]}&, {1, 10}, 10]][[1]] (* Harvey P. Dale, Oct 16 2011 *)
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PROG
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(Haskell)
a036299 n = a036299_list !! n
a036299_list = map read rabbits :: [Integer] where
rabbits = "1" : "10" : zipWith (++) (tail rabbits) rabbits
-- Reinhard Zumkeller, Jul 06 2014
(Python)
def aupton(terms):
alst = [1, 10]
while len(alst) < terms: alst.append(int(str(alst[-1]) + str(alst[-2])))
return alst[:terms]
print(aupton(9)) # Michael S. Branicky, Jan 10 2021
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CROSSREFS
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Cf. A005614, A003849.
Column k=10 of A144287.
Sequence in context: A324083 A162849 A041182 * A061107 A015498 A266283
Adjacent sequences: A036296 A036297 A036298 * A036300 A036301 A036302
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KEYWORD
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nonn,easy,nice,base
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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