

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
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OFFSET

0,2


COMMENTS

SpragueGrundy 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: nonattacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.
A. Dress, A. Flammenkamp and N. Pink, Additive periodicity of the SpragueGrundy function of certain Nim games, Adv. Appl. Math., 22, p. 249270 (1999).
Gabriel Nivasch, More on the SpragueGrundy function for Wythoff’s game, pages 377410 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



