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

Author

Hieronymus Fischer, Oct 10 2007

Keywords

• nonn
• easy

Comments

Periodic with length 3^2=9.

Links

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

Crossrefs

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

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

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.