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A005687
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Number of Twopins positions.
(Formerly M1004)
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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
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OFFSET
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7,2
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REFERENCES
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R. K. Guy, ``Anyone for Twopins?,'' in D. A. Klarner, editor, The Mathematical Gardner. Prindle, Weber and Schmidt, Boston, 1981, pp. 2-15.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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R. K. Guy, Anyone for Twopins?, in D. A. Klarner, editor, The Mathematical Gardner. Prindle, Weber and Schmidt, Boston, 1981, pp. 2-15. [Annotated scanned copy, with permission]
Index entries for linear recurrences with constant coefficients, signature (2, 0, -2, 1, 2, -2, 0, 0, 0, -1).
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FORMULA
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G.f.: x^7/((1-x^2-x^5)*(1-2*x+x^2-x^5)). - Simon Plouffe in his 1992 dissertation.
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MAPLE
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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); # Alois P. Heinz, Aug 14 2008
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MATHEMATICA
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LinearRecurrence[{2, 0, -2, 1, 2, -2, 0, 0, 0, -1}, {1, 2, 4, 6, 9, 14, 22, 36, 57, 90}, 40] (* Jean-François Alcover, Nov 12 2015 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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