login
A010876
a(n) = n mod 7.
35
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
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
KEYWORD
nonn,easy
EXTENSIONS
Formula section re-edited for better readability by Hieronymus Fischer, Dec 05 2011
STATUS
approved