



2, 0, 1, 5, 3, 4, 8, 6, 7, 11, 9, 10, 14, 12, 13, 17, 15, 16, 20, 18, 19, 23, 21, 22, 26, 24, 25, 29, 27, 28, 32, 30, 31, 35, 33, 34, 38, 36, 37, 41, 39, 40, 44, 42, 43, 47, 45, 46, 50, 48, 49, 53, 51, 52, 56, 54, 55, 59, 57, 58, 62, 60, 61, 65, 63, 64, 68, 66, 67
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OFFSET

0,1


COMMENTS

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.
Also 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..68.
A. Dress, A. Flammenkamp and N. Pink, Additive periodicity of the SpragueGrundy function of certain Nim games, Adv. Appl. Math., 22, p. 249270 (1999).
Index entries for linear recurrences with constant coefficients, signature (1,0,1,1).


FORMULA

Periodic with period and saltus 3: a(n) = 3[ n/3 ] + ((n+2) mod 3).
a(n)= 2 + Sum_{k=0..n}{1/3*(2*(k mod 3)2*((k+1) mod 3)+7*((k+2) mod 3)}, with n>=0  Paolo P. Lava, Oct 26 2007
a(n) = n + 2*cos(2*n*Pi/3).  Wesley Ivan Hurt, Sep 27 2017
G.f.: ( 2+x^2+2*x^32*x ) / ( (1+x+x^2)*(x1)^2 ). a(n) = n+A099837(n) if n>0. R. J. Mathar, Dec 14 2017


MATHEMATICA

a[n_] := If[Divisible[n, 3], n+2, n1]; Table[a[n], {n, 0, 70}] (* JeanFrançois Alcover, Oct 25 2013 *)
LinearRecurrence[{1, 0, 1, 1}, {2, 0, 1, 5}, 70] (* Harvey P. Dale, Feb 07 2018 *)


CROSSREFS

This sequence is row 2 of table A004481.
Second column of triangle in A296339.
Sequence in context: A163940 A112340 A037186 * A197808 A085650 A201910
Adjacent sequences: A004480 A004481 A004482 * A004484 A004485 A004486


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


EXTENSIONS

Edited by N. J. A. Sloane at the suggestion of Philippe Deléham, Nov 20 2007


STATUS

approved



