A005688 Numbers of Twopins positions. (Formerly M0647)

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

Table of n, a(n) for n=5..41.

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).

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

Adjacent sequences: A005685 A005686 A005687 * A005689 A005690 A005691

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

More terms from Johannes W. Meijer, Aug 24 2013

Status

approved