A010880 a(n) = n mod 11.
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, 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, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,1).
Crossrefs
Programs
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Mathematica
PadRight[{},80,Range[0,10]] (* Harvey P. Dale, Nov 13 2012 *) -
PARI
a(n)=n%11 \\ Charles R Greathouse IV, Oct 07 2015
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Sage
[power_mod(n,11,11) for n in range(0, 78)] # Zerinvary Lajos, Nov 07 2009
Formula
From Hieronymus Fischer, Sep 30 2007: (Start)
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).
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}}.
G.f.: (sum{1<=k<11, k*x^k})/(1-x^11).
G.f.: x*(10*x^11-11*x^10+1)/((1-x^11)*(1-x)^2). (End)
Extensions
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).