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

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

a(n) = floor(7625/274514*7^(n+1)) mod 7. - Hieronymus Fischer, Jan 04 2013

Prog

(Sage) [power_mod(n, 7, 7) for n in range(0, 81)] # Zerinvary Lajos, Nov 07 2009
(PARI) a(n)=n%7 \\ Charles R Greathouse IV, Dec 05 2011
(Magma) &cat [[0..6]^^20]; // Bruno Berselli, Jun 09 2016

Crossrefs

Partial sums: A130485.

Other related sequences: A130481, A130482, A130483, A130484.

Sequence in context: A037885 A347729 A031007 * A309958 A055400 A367842

Adjacent sequences: A010873 A010874 A010875 * A010877 A010878 A010879

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Formula section re-edited for better readability by Hieronymus Fischer, Dec 05 2011

Status

approved