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a(n) = n mod 7.
35

%I #37 Sep 08 2022 08:44:37

%S 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,

%T 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,

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

%N a(n) = n mod 7.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,1).

%F 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).

%F 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.

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

%F G.f.: x*(6*x^7-7*x^6+1)/((1-x^7)*(1-x)^2). - _Hieronymus Fischer_, May 31 2007

%F a(n) = floor(41152/3333333*10^(n+1)) mod 10. - _Hieronymus Fischer_, Jan 03 2013

%F a(n) = floor(7625/274514*7^(n+1)) mod 7. - _Hieronymus Fischer_, Jan 04 2013

%o (Sage) [power_mod(n,7,7) for n in range(0, 81)] # _Zerinvary Lajos_, Nov 07 2009

%o (PARI) a(n)=n%7 \\ _Charles R Greathouse IV_, Dec 05 2011

%o (Magma) &cat [[0..6]^^20]; // _Bruno Berselli_, Jun 09 2016

%Y Partial sums: A130485.

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

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_

%E Formula section re-edited for better readability by _Hieronymus Fischer_, Dec 05 2011