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A005691
Number of Twopins positions.
(Formerly M0643)
3
1, 2, 3, 5, 7, 10, 13, 18, 24, 35, 50, 75, 109, 161, 231, 336, 482, 703, 1020, 1498, 2188, 3214, 4694, 6877, 10039, 14699, 21487, 31489, 46097, 67582, 98977, 145071, 212463, 311344, 456045, 668328, 979182, 1435107, 2102900, 3082037, 4516347, 6618985, 9699527, 14215176
OFFSET
6,2
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, a(4) = 1 and a(5) = 1. The formula for a(n) confirms these values. - Johannes W. Meijer, Aug 26 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^6*(1-x^2+x^3-2*x^6-x^7-x^8-x^9-x^10-x^11))/((x^3-x+1)*(x^3+x-1)*(x^6+x^2-1)). - Ralf Stephan, Apr 22 2004
a(n) = Sum_{k=0..floor((n-1)/2)} A228570(n-1, 2*k), n >= 6. - Johannes W. Meijer, Aug 26 2013
MATHEMATICA
CoefficientList[Series[((1 - x^2 + x^3 - 2*x^6 - x^7 - x^8 - x^9 - x^10 - x^11))/((x^3 - x + 1) (x^3 + x - 1) (x^6 + x^2 - 1)), {x, 0, 50}], x] (* Wesley Ivan Hurt, May 03 2017 *)
CROSSREFS
Cf. A228570.
Sequence in context: A038083 A238863 A060688 * A035954 A023192 A064480
KEYWORD
nonn
EXTENSIONS
Extended by Johannes W. Meijer, Aug 26 2013
STATUS
approved