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A005682
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Number of Twopins positions.
(Formerly M1106)
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3
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1, 2, 4, 8, 15, 28, 51, 92, 165, 294, 522, 924, 1632, 2878, 5069, 8920, 15686, 27570, 48439, 85080, 149405, 262320, 460515, 808380, 1418916, 2490432, 4370944, 7671188, 13462945, 23627078, 41464296, 72766972, 127700055, 224101844, 393276447, 690158844, 1211153337
(list; graph; refs; listen; history; internal format)
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OFFSET
| 5,2
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REFERENCES
| 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
| 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.
Index to sequences with linear recurrences with constant coefficients, signature (2,0,0,-1,0,-1).
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FORMULA
| a(n)=2a(n-1)-a(n-4)-a(n-6) - John W. Layman (layman(AT)math.vt.edu).
G.f.: x^5/((x^3+x^2-1)*(x^3-x^2+2*x-1)). - Ralf Stephan, Apr 22 2004
a(n) = (A005251(n+1)-A000931(n+5))/2. - R. J. Mathar, Dec 10 2011
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MAPLE
| A005682:=1/((z**3-z**2+2*z-1)*(z**3+z**2-1)); [Conjectured (correctly) by S. Plouffe in his 1992 dissertation for offset 0]
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CROSSREFS
| Sequence in context: A006727 A182725 A029907 * A114833 A065617 A062065
Adjacent sequences: A005679 A005680 A005681 * A005683 A005684 A005685
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net).
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