A133876 n modulo 6 repeated 6 times.

1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 0, 0, 0

Offset

0,7

Comments

Periodic with length 6^2=36.

Links

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

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

Formula

a(n)=(1+floor(n/6)) mod 6.

a(n)=1+floor(n/6)-6*floor((n+6)/36).

a(n)=(((n+6) mod 36)-(n mod 6))/6.

a(n)=((n+6-(n mod 6))/6) mod 6.

G.f. g(x)=(1-x^6)(1+2x^5+3x^12+4x^18+5x^24)/((1-x)(1-x^36)).

G.f. g(x)=(5x^36-6x^30+1)/((1-x)(1-x^6)(1-x^36)).

Mathematica

Table[PadRight[{}, 6, Mod[n, 6]], {n, 20}]//Flatten (* Harvey P. Dale, Nov 15 2023 *)

Crossrefs

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

Cf. A133886, A133880, A133890, A133900, A133910.

Sequence in context: A071538 A321017 A138194 * A321018 A340764 A152467

Adjacent sequences: A133873 A133874 A133875 * A133877 A133878 A133879

Keyword

nonn

Author

Hieronymus Fischer, Oct 10 2007

Status

approved