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A125922
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Sprague-Grundy values for octal game .316.
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0
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1, 2, 0, 2, 1, 2, 3, 0, 1, 0, 3, 0, 1, 2, 3, 2, 1, 2, 3, 0, 1, 0, 3, 0, 1, 2, 3, 2, 1, 2, 3, 0, 1, 0, 3, 0, 1, 2, 3, 2, 1, 2, 3, 0, 1, 0, 3, 0, 1, 2, 3, 2, 1, 2, 3, 0, 1, 0, 3, 0, 1, 2, 3, 2, 1, 2, 3, 0, 1, 0, 3, 0, 1, 2, 3, 2, 1, 2, 3, 0, 1, 0, 3, 0, 1, 2, 3, 2, 1, 2, 3, 0, 1, 0, 3, 0, 1, 2, 3
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OFFSET
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1,2
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COMMENTS
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The sequence is eventually periodic with period 12. The last exception is at n=3.
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REFERENCES
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E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982; see Chapter 4, p. 104.
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LINKS
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Table of n, a(n) for n=1..99.
Index entries for linear recurrences with constant coefficients, signature (0, 1, 0, 0, 0, -1, 0, 1).
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FORMULA
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a(n)=(1/66)*{-4*(n mod 12)+18*[(n+1) mod 12]-15*[(n+2) mod 12]+7*[(n+3) mod 12]-4*[(n+4) mod 12]+18*[(n+5) mod 12]-4*[(n+6) mod 12]-4*[(n+7) mod 12]+7*[(n+8) mod 12]+7*[(n+9) mod 12]-4*[(n+10) mod 12]-4*[(n+11) mod 12]}-3*[C(n^2,n+2) mod 2], with n>=0 [From Paolo P. Lava, Oct 22 2008]
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MATHEMATICA
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Join[{1, 2, 0}, LinearRecurrence[{0, 1, 0, 0, 0, -1, 0, 1}, {2, 1, 2, 3, 0, 1, 0, 3}, 96]] (* Ray Chandler, Aug 27 2015 *)
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CROSSREFS
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Sequence in context: A029222 A162350 A334305 * A283306 A182893 A206298
Adjacent sequences: A125919 A125920 A125921 * A125923 A125924 A125925
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KEYWORD
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nonn
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AUTHOR
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Richard Sabey, Jan 24 2007
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EXTENSIONS
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Corrected formula. - Paolo P. Lava, Oct 23 2008
Extended by Ray Chandler, Aug 27 2015
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STATUS
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approved
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