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Search: id:A005686
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| A005686 |
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Number of Twopins positions.
(Formerly M0267)
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+0
2
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| 0, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 8, 9, 12, 14, 18, 22, 27, 34, 41, 52, 63, 79, 97, 120, 149, 183, 228, 280, 348, 429, 531, 657, 811, 1005, 1240, 1536, 1897, 2347, 2902, 3587, 4438, 5484, 6785, 8386, 10372, 12824, 15856, 19609, 24242, 29981, 37066, 45837
(list; graph; listen)
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OFFSET
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0,7
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COMMENT
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Appears to be the pairwise sums of A001687. - R. Stephan, Apr 21 2004
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REFERENCES
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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.
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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a(n)=sum{k=0..floor(n/2), binomial(floor((n+3k-3)/5), k)} - Paul Barry (pbarry(AT)wit.ie), Jul 10 2004
G.f.: [x+x^2]/[1-x^2-x^5]. - R. Stephan, Apr 21 2004
a(n)=a(n-2)+a(n-5). - Michael Somos, Jul 15 2004
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MAPLE
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A005686:=-(z+1)*(z**3+z+1)/(-1+z**2+z**5); [Conjectured by S. Plouffe in his 1992 dissertation.]
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PROGRAM
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(PARI) a(n)=if(n<0, polcoeff((x^3+x^4)/(1+x^3-x^5)+x^-n*O(x), -n), polcoeff((x+x^2)/(1-x^2-x^5)+x^n*O(x), n)) /* Michael Somos, Jul 15 2004 */
(PARI) a(n)=sum(k=0, (n-1)\2, binomial((n+3*k-4)\5, k))
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CROSSREFS
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Cf. A001687.
Sequence in context: A096792 A015741 A015753 this_sequence A118082 A120160 A017980
Adjacent sequences: A005683 A005684 A005685 this_sequence A005687 A005688 A005689
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KEYWORD
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nonn
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AUTHOR
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njas
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EXTENSIONS
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More terms from Paul Barry (pbarry(AT)wit.ie), Jul 10 2004
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