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A004482 Tersum n + 1 (answer recorded in base 10). 8
1, 2, 0, 4, 5, 3, 7, 8, 6, 10, 11, 9, 13, 14, 12, 16, 17, 15, 19, 20, 18, 22, 23, 21, 25, 26, 24, 28, 29, 27, 31, 32, 30, 34, 35, 33, 37, 38, 36, 40, 41, 39, 43, 44, 42, 46, 47, 45, 49, 50, 48, 52, 53, 51, 55, 56, 54, 58, 59, 57, 61, 62 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Sprague-Grundy values for game of Wyt Queens.

REFERENCES

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

LINKS

Table of n, a(n) for n=0..61.

F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.

A. Dress, A. Flammenkamp and N. Pink, Additive periodicity of the Sprague-Grundy function of certain Nim games, Adv. Appl. Math., 22, p. 249-270 (1999).

Gabriel Nivasch, More on the Sprague-Grundy function for Wythoff’s game, pages 377-410 in "Games of No Chance 3, MSRI Publications Volume 56, 2009. See Table 1.

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

FORMULA

Tersum m + n: write m and n in base 3 and add mod 3 with no carries, e.g. 5 + 8 = "21" + "22" = "10" = 1.

Periodic with period 3 and saltus 3: a(n) = 3[n/3] + ((n+1) mod 3).

a(n)= -3 + Sum_{k=0..n}{1/3*(-5*(k mod 3)+4*((k+1) mod 3)+4*((k+2) mod 3)}, with n>=0. - Paolo P. Lava, Dec 03 2007

a(n) = n - 2*cos(2*(n+1)*Pi/3). - Wesley Ivan Hurt, Sep 29 2017

MATHEMATICA

LinearRecurrence[{1, 0, 1, -1}, {1, 2, 0, 4}, 70] (* or *) Table[3*Floor[n/3]+ Mod[ n+1, 3], {n, 0, 70}] (* Harvey P. Dale, Nov 29 2014 *)

CROSSREFS

This sequence is row 1 of table A004481.

a(n) = A061347(n+1) + n.

Third column of triangle A296339.

Sequence in context: A335118 A201837 A326052 * A329233 A111677 A326186

Adjacent sequences: A004479 A004480 A004481 * A004483 A004484 A004485

KEYWORD

nonn,easy,base

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Erich Friedman

STATUS

approved

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Last modified December 3 09:39 EST 2022. Contains 358517 sequences. (Running on oeis4.)