A133873 n modulo 3 repeated 3 times.

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

Offset

0,4

Comments

Periodic with length 3^2=9.

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

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

Formula

G.f.: (1 + 2*x^3)*(1 - x^3)/((1 - x)*(1 - x^9)).

a(n) = (1 + floor(n/3)) mod 3.

a(n) = A010872(A002264(n+3)).

a(n) = 1+floor(n/3)-3*floor((n+3)/9).

a(n) = (((n+3) mod 9)-(n mod 3))/3.

a(n) = ((n+3-(n mod 3))/3) mod 3.

a(n) = binomial(n+3,n) mod 3 = binomial(n+3,3) mod 3.

Mathematica

Mod[Quotient[Range[0, 107], 3] + 1, 3] (* Paolo Xausa, May 25 2026 *)

Crossrefs

Cf. A000040, A133620-A133625, A133630, A038509, A133634-A133636.

Cf. A133883, A133880, A133890, A133900, A133910.

Sequence in context: A132784 A180834 A214458 * A163326 A028953 A348648

Adjacent sequences: A133870 A133871 A133872 * A133874 A133875 A133876

Keyword

nonn,easy

Author

Hieronymus Fischer, Oct 10 2007

Status

approved