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A005687 Number of Twopins positions.
(Formerly M1004)
0
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 (list; graph; refs; listen; history; text; internal format)
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.

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

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: A038718 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

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Last modified January 23 18:45 EST 2022. Contains 350514 sequences. (Running on oeis4.)