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Search: id:A046699
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| A046699 |
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a(1) = a(2) = 1, a(n) = a(n - a(n-1)) + a(n-1 - a(n-2)) if n > 2. |
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+0
4
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| 1, 1, 2, 2, 3, 4, 4, 4, 5, 6, 6, 7, 8, 8, 8, 8, 9, 10, 10, 11, 12, 12, 12, 13, 14, 14, 15, 16, 16, 16, 16, 16, 17, 18, 18, 19, 20, 20, 20, 21, 22, 22, 23, 24, 24, 24, 24, 25, 26, 26, 27, 28, 28, 28, 29, 30, 30, 31, 32, 32, 32, 32, 32, 32, 33, 34, 34, 35, 36, 36, 36, 37
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Ignoring first term, this is the Meta-Fibonacci sequence for s=0. - Frank Ruskey (http://www.cs.uvic.ca/~ruskey/) and Chris Deugau (deugaucj(AT)uvic.ca)
Except for first term, n occurs A001511(n) times. - Franklin T. Adams-Watters, Oct 22 2006
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REFERENCES
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Sequence proposed by Reg Allenby.
B. Jackson and F. Ruskey, Meta-Fibonacci Sequences, Binary Trees and Extremal Compact Codes, Electronic Journal of Combinatorics, 13 (2006), #R26, 13 pages.
S. Vajda, Fibonacci and Lucas Numbers and the Golden Section, Wiley, 1989, see p. 129.
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 129.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
C. Deugau and F. Ruskey, Complete k-ary Trees and Generalized Meta-Fibonacci Sequences, J. Integer Seq., Vol. 12. [This is a later version than that in the GenMetaFib.html link]
Joerg Arndt, Fxtbook
C. Deugau and F. Ruskey, Complete k-ary Trees and Generalized Meta-Fibonacci Sequences
B. Jackson and F. Ruskey, Meta-Fibonacci Sequences, Binary Trees and Extremal Compact Codes
Index entries for Hofstadter-type sequences
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FORMULA
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First differences seem to be A079559. - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 30 2003. This is correct and not too hard to prove, giving the generating function x + x^2(1+x)(1+x^3)(1+x^7)(1+x^15).../(1-x). - Paul Boddington (psb(AT)maths.warwick.ac.uk), Jul 30 2004
G.f. x + x^2/(1-x) * Product_{n=1}^{infinity} (1 + x^(2^n-1)) - Frank Ruskey (http://www.cs.uvic.ca/~ruskey/) and Chris Deugau (deugaucj(AT)uvic.ca)
for n>=1, a(n)=w(n-1) where w(n) is the least k such that 2^n divides (2k)! - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 19 2007
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MAPLE
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a := proc(n) option remember; if n <= 1 then return 1 end if; if n <= 2 then return 2 end if; return add(a(n - i + 1 - a(n - i)), i = 1 .. 2) end proc - Frank Ruskey (http://www.cs.uvic.ca/~ruskey/) and Chris Deugau (deugaucj(AT)uvic.ca)
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PROGRAM
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(PARI) a(n)=if(n<0, 1, s=1; while((2*s)!%2^(n-1)>0, s++); s) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 19 2007
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CROSSREFS
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Cf. A005185.
Adjacent sequences: A046696 A046697 A046698 this_sequence A046700 A046701 A046702
Sequence in context: A029111 A092038 A159481 this_sequence A102548 A004001 A086841
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KEYWORD
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nonn,nice
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AUTHOR
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R. K. Guy (rkg(AT)cpsc.ucalgary.ca)
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EXTENSIONS
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There are good arguments for dropping the first term, but I am reluctant to do this for a sequence with so many references. - N. J. A. Sloane (njas(AT)research.att.com), Oct 22 2006
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