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.
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
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).
Crossrefs
Presumably equals A048590(n-3) - 3, n>3.
Programs
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Maple
A003411:=-(1+z+z**2+z**3+z**4)/(-1+z+z**4); # Conjectured by Simon Plouffe in his 1992 dissertation
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Mathematica
Join[{1}, LinearRecurrence[{1, 0, 0, 1}, {2, 3, 4, 6}, 80]] (* Vladimir Joseph Stephan Orlovsky, Feb 11 2012 *)
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).