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Search: id:A005689
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| A005689 |
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Number of Twopins positions.
(Formerly M1042)
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+0
2
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| 1, 2, 4, 7, 11, 16, 22, 30, 42, 61, 91, 137, 205, 303, 443, 644, 936, 1365, 1999, 2936, 4316, 6340, 9300, 13625, 19949, 29209, 42785, 62701, 91917, 134758, 197548, 289547
(list; graph; listen)
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OFFSET
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6,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
R. Austin and R. K. Guy, Binary sequences without isolated ones, Fib. Quart., 16 (1978), 84-86.
R. K. Guy, ``Anyone for Twopins?,'' in D. A. Klarner, editor, The Mathematical Gardner. Prindle, Weber and Schmidt, Boston, 1981, pp. 2-15.
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LINKS
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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.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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G.f.: (1+x^2+x^3+x^4+x^5)/(1-2x+x^2-x^6). - R. Stephan, Apr 20 2004
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
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MAPLE
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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.]
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CROSSREFS
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Adjacent sequences: A005686 A005687 A005688 this_sequence A005690 A005691 A005692
Sequence in context: A000124 A152947 A098574 this_sequence A131075 A133523 A114805
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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