Search: id:A005689
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%I A005689 M1042
%S A005689 1,2,4,7,11,16,22,30,42,61,91,137,205,303,443,644,936,1365,1999,2936,
%T A005689 4316,6340,9300,13625,19949,29209,42785,62701,91917,134758,197548,289547
%N A005689 Number of Twopins positions.
%D A005689 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005689 S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques 
               Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%D A005689 R. Austin and R. K. Guy, Binary sequences without isolated ones, Fib. 
               Quart., 16 (1978), 84-86.
%D A005689 R. K. Guy, ``Anyone for Twopins?,'' in D. A. Klarner, editor, The Mathematical 
               Gardner. Prindle, Weber and Schmidt, Boston, 1981, pp. 2-15.
%H A005689 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A005689 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%F A005689 G.f.: (1+x^2+x^3+x^4+x^5)/(1-2x+x^2-x^6). - R. Stephan, Apr 20 2004
%F A005689 Sum{k=0..floor(n/6), binomial(n-4k, 2k)} is 1, 1, 1, 1, 1, 1, 2, 4, 7, 
               11, ... - Paul Barry (pbarry(AT)wit.ie), Sep 16 2004
%p A005689 A005689:=-(1+z**2+z**3+z**4+z**5)/(z**3+z-1)/(z**3-z+1); [Conjectured 
               by S. Plouffe in his 1992 dissertation.]
%Y A005689 Sequence in context: A000124 A152947 A098574 this_sequence A131075 A133523 
               A114805
%Y A005689 Adjacent sequences: A005686 A005687 A005688 this_sequence A005690 A005691 
               A005692
%K A005689 nonn
%O A005689 6,2
%A A005689 N. J. A. Sloane (njas(AT)research.att.com).

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