Search: id:A079559
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%I A079559
%S A079559 1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,
%T A079559 1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,1,0,0,
%U A079559 1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,1,1,0,1
%N A079559 Number of partitions of n into distinct parts of the form 2^j-1, j=1,
               2,....
%C A079559 Differences of the Meta-Fibonacci sequence for s=0. - Frank Ruskey (http:/
               /www.cs.uvic.ca/~ruskey/) and Chris Deugau (deugaucj(AT)uvic.ca)
%C A079559 Fixed point of morphism 0-->0, 1-->110 - Joerg Arndt (arndt(AT)jjj.de), 
               Jun 07 2007
%C A079559 Also, the infinite word generated by 1 -> 110, 0 -> 0. A006697(k) gives 
               number of distinct subwords of length k, conjectured to be equal 
               to A094913(k)+1. - M. F. Hasler, Dec 19 2007
%C A079559 Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Mar 18 2009: (Start)
%C A079559 Characteristic function for the range of A005187: a(A055938(n))=0; a(A005187(n))=1;
%C A079559 if a(m)=1 then either a(m-1)=1 or a(m+1)=1. (End)
%D A079559 B. Jackson and F. Ruskey, Meta-Fibonacci Sequences, Binary Trees and 
               Extremal Compact Codes, Electronic Journal of Combinatorics, 13 (2006), 
               #R26, 13 pages.
%H A079559 R. Zumkeller, <a href="b079559.txt">Table of n, a(n) for n = 0..1000</
               a> [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 
               18 2009]
%H A079559 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 A079559 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Fxtbook</a>
%H A079559 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 A079559 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 A079559 <a href="Sindx_Ch.html#char_fns">Index entries for characteristic functions</
               a> [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 
               18 2009]
%F A079559 G.f.: Product_{n>0} 1+x^(2^n-1).
%F A079559 a(n) = if n=0 then 1 else A043545(n+1)*a(n-A053644(n)). - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Aug 19 2006
%F A079559 a(n) = p(n,1) with p(n,k) = if k<=n then p(n-k,2*k+1)+p(n,2*k+1) else 
               0^n. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Mar 18 2009]
%F A079559 Euler transform is sequence A111113 sequence offset -1. - Michael Somos 
               Aug 03 2009
%F A079559 G.f.: Product_{k>0} (1 - x^k)^-A111113(k+1). - Michael Somos Aug 03 2009
%e A079559 a(11)=1 because we have [7,3,1].
%e A079559 1 + x + x^3 + x^4 + x^7 + x^8 + x^10 + x^11 + x^15 + x^16 + x^18 + ...
%p A079559 g:=product(1+x^(2^n-1),n=1..15): gser:=series(g,x=0,110): seq(coeff(gser,
               x,n),n=0..104); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 
               06 2006
%p A079559 d := n -> if n=1 then 1 else A046699(n)-A046699(n-1) fi; - Frank Ruskey 
               (http://www.cs.uvic.ca/~ruskey/) and Chris Deugau (deugaucj(AT)uvic.ca)
%o A079559 (PARI) w="1,";for(i=1,5,print1(w=concat([w,w,"0,"])))
%o A079559 (PARI) A079559(n,w=[1])=until(n<#w=concat([w,w,[0]]),);w[n+1] \\- M. 
               F. Hasler, Dec 19 2007
%o A079559 (PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, #binary(n+1), 1 + x^(2^k-1), 
               1 + x * O(x^n)), n))} /* Michael Somos Aug 03 2009 */
%Y A079559 Cf. A005187, A055938, A000929, A046699, A006697, A094913.
%Y A079559 Sequence in context: A145006 A080813 A100672 this_sequence A014577 A157926 
               A131377
%Y A079559 Adjacent sequences: A079556 A079557 A079558 this_sequence A079560 A079561 
               A079562
%K A079559 nonn
%O A079559 0,1
%A A079559 Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 25 2003
%E A079559 Edited by M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Jan 03 2008

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