A010880 - OEIS (original) (raw)

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

LINKS

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,1).

FORMULA

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)

MATHEMATICA

PadRight[{}, 80, Range[0, 10]] (* Harvey P. Dale, Nov 13 2012 *)

PROG

(SageMath) [power_mod(n, 11, 11) for n in range(0, 78)] # Zerinvary Lajos, Nov 07 2009

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).