A133879 n modulo 9 repeated 9 times.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3

Offset

0,10

Comments

Periodic with length 9^2=81.

Links

Table of n, a(n) for n=0..104.

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

Formula

a(n)=(1+floor(n/9)) mod 9.

a(n)=1+floor(n/9)-9*floor((n+9)/81).

a(n)=(((n+9) mod 81)-(n mod 9))/9.

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

G.f. g(x)=(1-x^9)(1+2x^9+3x^18+4x^27+5x^36+6x^45+7x^56+8x^63)/((1-x)(1-x^81)).

G.f. g(x)=(1-x^9)*sum{0<=k<8, (k+1)*x^(9*k)}/((1-x)(1-x^81)).

G.f. g(x)=(8x^81-9x^72+1)/((1-x)(1-x^9)(1-x^81)).

Mathematica

Rest[Flatten[Table[Table[Table[n, {9}], {n, 0, 8}], {3}], 1]]//Flatten (* Harvey P. Dale, Apr 15 2018 *)

Crossrefs

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

Cf. A133889, A133880, A133890, A133900, A133910.

Sequence in context: A111858 A111856 A111857 * A343609 A054898 A279951

Adjacent sequences: A133876 A133877 A133878 * A133880 A133881 A133882

Keyword

nonn

Author

Hieronymus Fischer, Oct 10 2007

Status

approved