A125916 Sprague-Grundy values for octal game .15 (Guiles).

0, 1, 1, 0, 1, 1, 2, 2, 1, 2, 2, 1, 1, 0, 1, 1, 2, 2, 1, 2, 2, 1, 1, 0, 1, 1, 2, 2, 1, 2, 2, 1, 1, 0, 1, 1, 2, 2, 1, 2, 2, 1, 1, 0, 1, 1, 2, 2, 1, 2, 2, 1, 1, 0, 1, 1, 2, 2, 1, 2, 2, 1, 1, 0, 1, 1, 2, 2, 1, 2, 2, 1, 1, 0, 1, 1, 2, 2, 1, 2, 2, 1, 1, 0, 1, 1, 2, 2, 1, 2, 2, 1, 1, 0, 1, 1, 2, 2, 1, 2, 2

Offset

0,7

Comments

After the initial 0 the sequence is periodic with period 10.

This game is called "Guiles" in Winning Ways.

References

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982; see Chapter 4, p. 104.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

R. K. Guy and C. A. B. Smith, The G-values of various games, Proc. Cambridge Philos. Soc. 52 (1956), 514-526. See Table 2.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Formula

From Colin Barker, Apr 02 2019: (Start)

G.f.: x*(1 + x + x^3 + x^4 + 2*x^5 + 2*x^6 + x^7 + 2*x^8 + 2*x^9) / ((1 - x)*(1 + x)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)).

a(n) = a(n-10) for n>10.

(End)

Mathematica

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 1, 1, 0, 1, 1, 2, 2, 1, 2, 2}, 100] (* Ray Chandler, Aug 26 2015; offset 0 corrected by Georg Fischer, Apr 02 2019 *)

Prog

(PARI) concat(0, Vec(x*(1 + x + x^3 + x^4 + 2*x^5 + 2*x^6 + x^7 + 2*x^8 + 2*x^9) / ((1 - x)*(1 + x)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)) + O(x^80))) \\ Colin Barker, Apr 02 2019

Crossrefs

Sequence in context: A300480 A342870 A143537 * A283468 A100244 A059689

Adjacent sequences: A125913 A125914 A125915 * A125917 A125918 A125919

Keyword

nonn,easy

Author

Richard Sabey, Jan 24 2007

Extensions

Extended by Ray Chandler, Aug 26 2015

Added initial 0 and changed offset. - N. J. A. Sloane, Jul 02 2016

Status

approved