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Search: id:A005687
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| A005687 |
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Number of Twopins positions.
(Formerly M1004)
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+0
1
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| 1, 2, 4, 6, 9, 14, 22, 36, 57, 90, 139, 214, 329, 506, 780, 1200, 1845, 2830, 4337, 6642, 10170, 15572, 23838, 36486, 55828, 85408, 130641, 199814, 305599, 467366, 714735, 1092980, 1671335, 2555650, 3907781, 5975202, 9136288, 13969560, 21359528
(list; graph; listen)
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OFFSET
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7,2
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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).
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.: [x^7]/[(1-x^2-x^5)(1-2x+x^2-x^5)]. - Ralf Stephan, Apr 22 2004
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MAPLE
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A005687:=1/(z**5-z**2+2*z-1)/(-1+z**2+z**5); [Conjectured by S. Plouffe in his 1992 dissertation.]
a := n-> (Matrix(10, (i, j)-> if (i=j-1) then 1 elif j=1 then [2, 0, -2, 1, 2, -2, 0, 0, 0, -1][i] else 0 fi)^n)[1, 8]; seq (a(n), n=7..70); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 14 2008]
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CROSSREFS
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Sequence in context: A119737 A038718 A042942 this_sequence A164139 A024849 A090483
Adjacent sequences: A005684 A005685 A005686 this_sequence A005688 A005689 A005690
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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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EXTENSIONS
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More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 14 2008
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