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A005688
Numbers of Twopins positions.
(Formerly M0647)
1
1, 2, 3, 5, 7, 10, 14, 20, 30, 45, 69, 104, 157, 236, 356, 540, 821, 1252, 1908, 2909, 4434, 6762, 10319, 15755, 24066, 36766, 56176, 85837, 131172, 200471, 306410, 468371, 715975, 1094516, 1673232, 2557997, 3910683
OFFSET
5,2
COMMENTS
The complete sequence by R. K. Guy in "Anyone for Twopins?" starts with a(0) = 0, a(1) = 1, a(2) = 1, a(3) = 1 and a(4) =1. The formula for a(n) confirms these values. - Johannes W. Meijer, Aug 24 2013
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).
LINKS
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]
FORMULA
G.f.: (x^5*(1-x^2+x^3-2*x^5-x^6-x^7-x^8-x^9))/((1-x^2-x^5)*(1-2*x+x^2-x^5)). - Ralf Stephan, Apr 22 2004
a(n) = sum(A102541(n-k-1, 2*k), k=0..floor((n-1)/3)), n >= 5. - Johannes W. Meijer, Aug 24 2013
MATHEMATICA
LinearRecurrence[{2, 0, -2, 1, 2, -2, 0, 0, 0, -1}, {1, 2, 3, 5, 7, 10, 14, 20, 30, 45}, 40] (* Harvey P. Dale, Aug 26 2019 *)
CROSSREFS
Sequence in context: A094984 A107332 A002062 * A241550 A319564 A347869
KEYWORD
nonn,easy
EXTENSIONS
More terms from Johannes W. Meijer, Aug 24 2013
STATUS
approved