A021105 - OEIS

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A021105

Decimal expansion of 1/101.

0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..98.

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

FORMULA

From Wesley Ivan Hurt, Jun 04 2016: (Start)

G.f.: 9*x^2/(1-x)*(1+x^2).

a(n) = a(n-1) - a(n-2) + a(n-3) for n>2.

a(n) = 9*(1+(-1)^((2*n+3+(-1)^n)/4))/2 = 9*A133872(n+2).

a(n) = 9*(1+i)*(1-i-i^(-n)+i^(1+n))/4 where i=sqrt(-1).