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A003413
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From a nim-like game.
(Formerly M0521)
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1
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1, 2, 3, 4, 5, 7, 9, 12, 15, 19, 24, 31, 40, 52, 67, 86, 110, 141, 181, 233, 300, 386, 496, 637, 818, 1051, 1351, 1737, 2233, 2870, 3688, 4739, 6090, 7827, 10060, 12930, 16618, 21357, 27447, 35274, 45334, 58264, 74882, 96239, 123686, 158960, 204294, 262558
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listen;
history;
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internal format)
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OFFSET
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0,2
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REFERENCES
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R. K. Guy, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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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, 0, 0, 1).
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FORMULA
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Recurrence: a(n) = a(n-1) + a(n-6) for n >= 8.
O.g.f.: -(x^2+x+1)*(x^5+x^3+1)/(-1+x+x^6) = -x-1+(-2-x-x^3-x^4-2*x^5)/(-1+x+x^6). - R. J. Mathar, Dec 05 2007
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MAPLE
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A003413:=-(z**5+z**3+1)*(z**2+z+1)/(z**6+z-1); # Simon Plouffe in his 1992 dissertation
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MATHEMATICA
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Join[{1, 2}, LinearRecurrence[{1, 0, 0, 0, 0, 1}, {3, 4, 5, 7, 9, 12}, 80]] (* Vladimir Joseph Stephan Orlovsky, Feb 11 2012 *)
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CROSSREFS
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Cf. A005708.
Sequence in context: A062188 A122129 A280909 * A100853 A174065 A121659
Adjacent sequences: A003410 A003411 A003412 * A003414 A003415 A003416
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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