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%I #30 Mar 04 2022 11:08:00
%S 0,1,2,3,4,5,6,7,8,9,10,0,1,2,3,4,5,6,7,8,9,10,0,1,2,3,4,5,6,7,8,9,10,
%T 0,1,2,3,4,5,6,7,8,9,10,0,1,2,3,4,5,6,7,8,9,10,0,1,2,3,4,5,6,7,8,9,10,
%U 0,1,2,3,4,5,6,7,8,9,10,0
%N a(n) = n mod 11.
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,1).
%F From _Hieronymus Fischer_, Sep 30 2007: (Start)
%F a(n) = (1/11)*(1-r^n)*sum{1<=k<11, k*product{1<=m<11,m<>k, (1-r^(n-m))}} where r=exp(2*Pi/11*i) and i=sqrt(-1).
%F a(n) = (1024/11)^2*(sin(n*Pi/11))^2*sum{1<=k<11, k*product{1<=m<11,m<>k, (sin((n-m)*Pi/11))^2}}.
%F G.f.: (sum{1<=k<11, k*x^k})/(1-x^11).
%F G.f.: x*(10*x^11-11*x^10+1)/((1-x^11)*(1-x)^2). (End)
%t PadRight[{},80,Range[0,10]] (* _Harvey P. Dale_, Nov 13 2012 *)
%o (Sage) [power_mod(n,11,11) for n in range(0, 78)] # _Zerinvary Lajos_, Nov 07 2009
%o (PARI) a(n)=n%11 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Partial sums: A130489. Other related sequences A130481, A130482, A130483, A130484, A130485, A130486, A130487, A130488.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from Correction. Typo at the sum formula for the g.f.: the summation index should not read "1<=k<10" but "1<=k<11" (see corrected formula).
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