A003413 From a nim-like game. (Formerly M0521)

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

Offset

0,2

References

R. K. Guy, personal communication.

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, 0, 0, 1).

Formula

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

Maple

A003413:=-(z**5+z**3+1)*(z**2+z+1)/(z**6+z-1); # Simon Plouffe in his 1992 dissertation

Mathematica

Join[{1, 2}, LinearRecurrence[{1, 0, 0, 0, 0, 1}, {3, 4, 5, 7, 9, 12}, 80]] (* Vladimir Joseph Stephan Orlovsky, Feb 11 2012 *)

Crossrefs

Cf. A005708.

Sequence in context: A062188 A122129 A280909 * A100853 A174065 A121659

Adjacent sequences: A003410 A003411 A003412 * A003414 A003415 A003416

Keyword

nonn

Author

N. J. A. Sloane

Status

approved