A133877 n modulo 7 repeated 7 times.

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

Offset

0,8

Comments

Periodic with length 7^2=49.

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

Formula

a(n)=(1+floor(n/7)) mod 7.

a(n)=1+floor(n/7)-7*floor((n+7)/49).

a(n)=(((n+7) mod 49)-(n mod 7))/7.

a(n)=((n+7-(n mod 7))/7) mod 7.

a(n)=binomial(n+7,n) mod 7 =binomial(n+7,7) mod 7.

G.f. g(x)=(1-x^7)(1+2x^7+3x^14+4x^21+5x^28+6x^35)/((1-x)(1-x^49)).

G.f. g(x)=(6x^49-7x^42+1)/((1-x)(1-x^7)(1-x^49)).

Crossrefs

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

Cf. A133887, A133880, A133890, A133900, A133910.

Sequence in context: A115338 A348522 A226046 * A132270 A195174 A187185

Adjacent sequences: A133874 A133875 A133876 * A133878 A133879 A133880

Keyword

nonn

Author

Hieronymus Fischer, Oct 10 2007

Status

approved