A004485 Sprague-Grundy values for game of Wyt Queens.

4, 5, 3, 2, 7, 6, 9, 0, 1, 8, 13, 12, 11, 16, 15, 10, 19, 18, 17, 14, 21, 20, 25, 24, 23, 28, 27, 22, 31, 30, 29, 26, 33, 32, 37, 36, 35, 40, 39, 34, 43, 42, 41, 38, 45, 44, 49, 48, 47, 52, 51, 46, 55, 54, 53, 50, 57, 56, 61, 60, 59, 64

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Inverse of sequence A064207 considered as a permutation of the nonnegative integers. - Howard A. Landman, Sep 25 2001

References

• E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 76.

Links

• A. Dress, A. Flammenkamp and N. Pink, Additive periodicity of the Sprague-Grundy function of certain Nim games, Adv. Appl. Math., 22, pp. 249-270 (1999).
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,1,-1).
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

This sequence is row 4 of table A004481.

Formula

Conjectures from Chai Wah Wu, Apr 05 2021: (Start)

a(n) = a(n-1) + a(n-12) - a(n-13) for n > 21.

G.f.: (-8*x^21 + 6*x^20 + 6*x^19 - 4*x^18 + 4*x^16 - 4*x^15 + x^14 + 4*x^13 - 5*x^12 - x^11 + 5*x^10 + 7*x^9 + x^8 - 9*x^7 + 3*x^6 - x^5 + 5*x^4 - x^3 - 2*x^2 + x + 4)/(x^13 - x^12 - x + 1). (End)

Extensions

More terms from Howard A. Landman