A005687 Number of Twopins positions. (Formerly M1004)

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

Offset

7,2

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=7..45.

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]

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Index entries for linear recurrences with constant coefficients, signature (2, 0, -2, 1, 2, -2, 0, 0, 0, -1).

Formula

G.f.: x^7/((1-x^2-x^5)*(1-2*x+x^2-x^5)). - Simon Plouffe in his 1992 dissertation.

2*a(n) = A005253(n-2) - A005686(n). - R. J. Mathar, May 29 2019

Maple

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

Mathematica

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 *)

Crossrefs

Sequence in context: A378307 A042942 A256968 * A164139 A218605 A024849

Adjacent sequences: A005684 A005685 A005686 * A005688 A005689 A005690

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Alois P. Heinz, Aug 14 2008

Status

approved