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A001964 Wythoff game.
(Formerly M4086 N1695)
2
1, 6, 11, 17, 22, 27, 32, 37, 43, 48, 53, 58, 64, 69, 74, 79, 85, 90, 95, 100, 106, 111, 116, 121, 126, 132, 137, 142, 147, 153, 158, 163, 168, 174, 179, 184, 189, 195, 200, 205, 210, 215, 221, 226, 231, 236, 242, 247, 252, 257, 263, 268, 273, 278, 284, 289 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

v-pile positions of the 4-Wythoff game with parameter i=1 (Connell nomenclature).

The g.f. (1+5*z+5*z**2+4*z**4+6*z**3-z**7+z**8)/(z+1)/(1+z**2)/(z-1)**2 conjectured by Simon Plouffe in his 1992 dissertation is wrong.

REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n = 0..10000

Ian G. Connell, A generalization of Wythoff's game, Canad. Math. Bull. 2 (1959) 181-190

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

FORMULA

a(n) = floor( (n+1/4)*(3+sqrt(5)) ). - R. J. Mathar, Feb 14 2011

MATHEMATICA

Table[Floor[(n + 1/4)*(Sqrt[5] + 3)], {n, 0, 100}] (* T. D. Noe, Aug 17 2012 *)

CROSSREFS

Cf. A001963 (u-pile).

Sequence in context: A118847 A111256 A221026 * A074993 A231001 A063901

Adjacent sequences:  A001961 A001962 A001963 * A001965 A001966 A001967

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 10 23:26 EST 2016. Contains 268159 sequences.