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A021823 Decimal expansion of 1/819. 13
0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Partial sums of A010892. - Paul Barry, Jun 06 2003

Expansion in any base b >= 3 of 1/((b-1)(b^2-b+1) = 1/(b^3-2b^2+2b-1). E.g., 1/14 in base 3, 1/39 in base 4, 1/84 in base 5, etc. - Franklin T. Adams-Watters, Nov 07 2006

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (2, -2, 1).

FORMULA

a(n) = a(n-1)-a(n-2)+1 = 2-a(n-3) = a(n-6). - Henry Bottomley, Apr 12 2000

a(n) = Sum_{k=1..floor(n/2)} (-1)^(k+1)*binomial(n-k, k) = 1-((-1)^floor(n/3)+(-1)^(floor((n+1)/3)))/2. - Vladeta Jovovic, Feb 10 2003

G.f.: x^2/(1-2x+2x^2-x^3)=x^2/((1-x)(x^2-x+1)). - Paul Barry, Jun 06 2003

a(n+2) = sum{k=0..n, binomial(n-2k, n-k)}. - Paul Barry, Jan 15 2005

a(n) = (1/30)*{7*(n mod 6)+7*[(n+1) mod 6]+2*[(n+2) mod 6]-3*[(n+3) mod 6]-3*[(n+4) mod 6]+2*[(n+5) mod 6]}, with n>=0. - Paolo P. Lava, Jan 31 2008

a(0)=0, a(1)=0, a(2)=1, a(n)=2*a(n-1)-2*a(n-2)+a(n-3). - Harvey P. Dale, Aug 19 2012

EXAMPLE

0.0012210012210012210...

MATHEMATICA

Join[{0, 0}, RealDigits[1/819, 10, 120][[1]]] (* or *) PadRight[{}, 120, {0, 0, 1, 2, 2, 1}] (* or *) LinearRecurrence[{2, -2, 1}, {0, 0, 1}, 120] (* Harvey P. Dale, Aug 19 2012 *)

PROG

(PARI) a(n)=1/819. \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Cf. A077859, A027444.

Sequence in context: A281497 A198243 A164965 * A131026 A333839 A014604

Adjacent sequences:  A021820 A021821 A021822 * A021824 A021825 A021826

KEYWORD

nonn,cons,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified January 25 06:09 EST 2021. Contains 340416 sequences. (Running on oeis4.)