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A021823
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Decimal expansion of 1/819.
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12
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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
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OFFSET
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0,4
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COMMENTS
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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
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LINKS
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Table of n, a(n) for n=0..98.
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FORMULA
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A077859.
Cf. A027444.
Sequence in context: A024712 A198243 A164965 * A131026 A014604 A015199
Adjacent sequences: A021820 A021821 A021822 * A021824 A021825 A021826
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KEYWORD
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nonn,cons,changed
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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