Search: id:A046699
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%I A046699
%S A046699 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,
%T A046699 16,16,16,16,17,18,18,19,20,20,20,21,22,22,23,24,24,24,24,25,26,26,
%U A046699 27,28,28,28,29,30,30,31,32,32,32,32,32,32,33,34,34,35,36,36,36,37
%N A046699 a(1) = a(2) = 1, a(n) = a(n - a(n-1)) + a(n-1 - a(n-2)) if n > 2.
%C A046699 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)
%C A046699 Except for first term, n occurs A001511(n) times. - Franklin T. Adams-Watters, 
               Oct 22 2006
%D A046699 Sequence proposed by Reg Allenby.
%D A046699 B. Jackson and F. Ruskey, Meta-Fibonacci Sequences, Binary Trees and 
               Extremal Compact Codes, Electronic Journal of Combinatorics, 13 (2006), 
               #R26, 13 pages.
%D A046699 S. Vajda, Fibonacci and Lucas Numbers and the Golden Section, Wiley, 
               1989, see p. 129.
%D A046699 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 129.
%H A046699 T. D. Noe, <a href="b046699.txt">Table of n, a(n) for n=1..1000</a>
%H A046699 C. Deugau and F. Ruskey, <a href="http://www.cs.uwaterloo.ca/journals/
               JIS/VOL12/Ruskey/ruskey6.pdf">Complete k-ary Trees and Generalized 
               Meta-Fibonacci Sequences</a>, J. Integer Seq., Vol. 12. [This is 
               a later version than that in the GenMetaFib.html link]
%H A046699 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Fxtbook</a>
%H A046699 C. Deugau and F. Ruskey, <a href="http://www.cs.uvic.ca/~ruskey/Publications/
               MetaFib/GenMetaFib.html">Complete k-ary Trees and Generalized Meta-Fibonacci 
               Sequences</a>
%H A046699 B. Jackson and F. Ruskey, <a href="http://www.cs.uvic.ca/~ruskey/Publications/
               MetaFib/MetaFib.html">Meta-Fibonacci Sequences, Binary Trees and 
               Extremal Compact Codes</a>
%H A046699 <a href="Sindx_Ho.html#Hofstadter">Index entries for Hofstadter-type 
               sequences</a>
%F A046699 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
%F A046699 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)
%F A046699 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
%p A046699 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)
%o A046699 (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
%Y A046699 Cf. A005185.
%Y A046699 Sequence in context: A029111 A092038 A159481 this_sequence A102548 A004001 
               A086841
%Y A046699 Adjacent sequences: A046696 A046697 A046698 this_sequence A046700 A046701 
               A046702
%K A046699 nonn,nice
%O A046699 1,3
%A A046699 R. K. Guy (rkg(AT)cpsc.ucalgary.ca)
%E A046699 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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