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A005203
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Fibonacci numbers (or rabbit sequence) converted to decimal.
(Formerly M1539)
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13
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0, 1, 2, 5, 22, 181, 5814, 1488565, 12194330294, 25573364166211253, 439347050970302571643057846, 15829145720289447797800874537321282579904181, 9797766637414564027586288536574448245991597197836000123235901011048118
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| J. L. Davison, A series and its associated continued fraction, Proc. Amer. Math. Soc., 63 (1977), 29-32.
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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| R. Knott, The Fibonacci Rabbit Sequence
R. Knott, Rabbit Sequence in Zeckendorf Expansion (A003714)
Eric Weisstein's World of Mathematics, Further Information
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FORMULA
| a(0) = 0, a(1) = 1, a(n) = a(n-1)*(2^Fib(n-1))+a(n-2)
a(n) = rewrite_0to1_1to10_n_i_times(0, n) [ Each 0->1, 1->10 in binary expansion ]
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MAPLE
| rewrite_0to1_1to10_n_i_times := proc(n, i) local z, j; z := n; j := i; while(j > 0) do z := rewrite_0to1_1to10(z); j := j - 1; od; RETURN(z); end;
rewrite_0to1_1to10 := proc(n) option remember; if(n < 2) then RETURN(n + 1); else RETURN(((2^(1+(n mod 2))) * rewrite_0to1_1to10(floor(n/2))) + (n mod 2) + 1); fi; end;
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MATHEMATICA
| a[0] = 0; a[1] = 1; a[n_] := a[n] = a[n-1]*2^Fibonacci[n-1] + a[n-2]; Table[a[n], {n, 0, 12}]
(* From Jean-François Alcover, Jul 27 2011 *)
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CROSSREFS
| Cf. A000045, A048707, A003714, A048721, A048722, A048678, A048679, A048680, A005205.
Sequence in context: A001437 A067549 A042933 * A193660 A090450 A137099
Adjacent sequences: A005200 A005201 A005202 * A005204 A005205 A005206
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Comments and more terms from Antti Karttunen, 30.3.1999
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