|
%I M0561 #41 Apr 13 2022 13:25:16
%S 1,2,3,4,6,8,11,15,21,29,40,55,76,105,145,200,276,381,526,726,1002,
%T 1383,1909,2635,3637,5020,6929,9564,13201,18221,25150,34714,47915,
%U 66136,91286,126000,173915,240051,331337,457337,631252,871303,1202640,1659977
%N 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.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A003411/b003411.txt">Table of n, a(n) for n = 0..1000</a>
%H R. K. Guy, <a href="/A003410/a003410.pdf">Letter to N. J. A. Sloane, Apr 1975</a>
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 1).
%F a(n) = a(n-1) + a(n-4), n >= 5.
%F G.f.: (1+x+x^2+x^3+x^4)/(1-x-x^4).
%p A003411:=-(1+z+z**2+z**3+z**4)/(-1+z+z**4); # Conjectured by _Simon Plouffe_ in his 1992 dissertation
%t Join[{1}, LinearRecurrence[{1, 0, 0, 1}, {2, 3, 4, 6}, 80]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 11 2012 *)
%Y Presumably equals A048590(n-3) - 3, n>3.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, _R. K. Guy_, Rodney W. Topor (rwt(AT)cit.gu.edu.au)
|
