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 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) 3
 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 (list; graph; refs; listen; history; text; internal format)
 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. 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

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Last modified April 15 23:51 EDT 2021. Contains 343018 sequences. (Running on oeis4.)