A003411 Losing initial positions in game: two players alternate in removing >= 1 stones; last player wins; first player may not remove all stones; each move <= 3 times previous move. (Formerly M0561)

1, 2, 3, 4, 6, 8, 11, 15, 21, 29, 40, 55, 76, 105, 145, 200, 276, 381, 526, 726, 1002, 1383, 1909, 2635, 3637, 5020, 6929, 9564, 13201, 18221, 25150, 34714, 47915, 66136, 91286, 126000, 173915, 240051, 331337, 457337, 631252, 871303, 1202640, 1659977

Offset

0,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

R. K. Guy, Letter to N. J. A. Sloane, Apr 1975

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 (1, 0, 0, 1).

Formula

a(n) = a(n-1) + a(n-4), n >= 5.

G.f.: (1+x+x^2+x^3+x^4)/(1-x-x^4).

Maple

A003411:=-(1+z+z**2+z**3+z**4)/(-1+z+z**4); # Conjectured by Simon Plouffe in his 1992 dissertation

Mathematica

Join[{1}, LinearRecurrence[{1, 0, 0, 1}, {2, 3, 4, 6}, 80]] (* Vladimir Joseph Stephan Orlovsky, Feb 11 2012 *)

Crossrefs

Presumably equals A048590(n-3) - 3, n>3.

Sequence in context: A014213 A341218 A064323 * A034081 A289432 A064660

Adjacent sequences: A003408 A003409 A003410 * A003412 A003413 A003414

Keyword

nonn,easy

Author

N. J. A. Sloane, R. K. Guy, Rodney W. Topor (rwt(AT)cit.gu.edu.au)

Status

approved