A010876 - OEIS

A010876

a(n) = n mod 7.

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

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..87.

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

FORMULA

Complex representation: a(n) = (1/7)*(1-r^n) * Sum_{1<=k<7} k * Product_{1<=m<7, m<>k} (1-r^(n-m)) where r=exp(2*pi/7*i) and i=sqrt(-1).

Trigonometric representation: a(n) = (64/7)^2*(sin(n*pi/7))^2*Sum_{1<=k<7} k*Product_{1<=m<7,m<>k} sin((n-m)*pi/7)^2.

G.f.: ( Sum_{1<=k<7} k*x^k ) / (1 - x^7).

G.f.: x*(6*x^7-7*x^6+1)/((1-x^7)*(1-x)^2). - Hieronymus Fischer, May 31 2007

a(n) = floor(41152/3333333*10^(n+1)) mod 10. - Hieronymus Fischer, Jan 03 2013