A133878 n modulo 8 repeated 8 times.

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

Offset

0,9

Comments

Periodic with length 8^2=64.

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, -1, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, 1).

Formula

a(n)=(1+floor(n/8)) mod 8.

a(n)=1+floor(n/8)-8*floor((n+8)/64).

a(n)=(((n+8) mod 64)-(n mod 8))/8.

a(n)=((n+8-(n mod 8))/8) mod 8.

G.f. g(x)=(1-x^8)(1+2x^8+3x^16+4x^24+5x^32+6x^40+7x^48)/((1-x)(1-x^64)).

G.f. g(x)=(1-x^8)*sum{0<=k<7, (k+1)*x^(8*k)}/((1-x)(1-x^64)).

G.f. g(x)=(7x^64-8x^56+1)/((1-x)(1-x^8)(1-x^64)).

Mathematica

Flatten[Join[Table[PadRight[{}, 8, n], {n, 7}], Table[PadRight[{}, 8, n], {n, 0, 7}]]] (* Harvey P. Dale, Nov 06 2011 *)

Crossrefs

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

Cf. A133888, A133880, A133890, A133900, A133910.

Sequence in context: A135664 A261585 A058318 * A132292 A110656 A104407

Adjacent sequences: A133875 A133876 A133877 * A133879 A133880 A133881

Keyword

nonn

Author

Hieronymus Fischer, Oct 10 2007

Status

approved