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A021913
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Periodic with period 4: repeat 0,0,1,1.
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17
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0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Decimal expansion of 1/909.
Lexicographically earliest de Bruijn sequence for n = 2 and k = 2.
Except for first term, binary expansion of the decimal number 1/10 = 0,000110011001100110011....in base 2 - Benoit Cloitre (benoit7848c(AT)orange.fr), May 18 2002
Content of #2 binary placeholder when n is converted from decimal to binary. a(n) = Mod(n*(n-1)/2,2). Example: a(7) = 1 since 7 in binary is 1 -1- 1 and (7*6/2) mod 2 = 1 - Anne M. Donovan (anned3005(AT)aol.com) Sep 15 2003
Expansion in any base b of 1/((b-1)(b^2+1)) = 1/(b^3-b^2+b-1). E.g., 1/5 in base 2, 1/20 in base 3, 1/51 in base 4, etc. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Nov 07 2006
Except for first term, parity of the triangular numbers A000217. - Omar E. Pol, Jan 17 2012
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LINKS
| Index entries for sequences related to Chebyshev polynomials.
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FORMULA
| G.f. : (x^2+x^3)/(1-x^4); a(n)=1/2-cos(pi*n/2)/2-sin(pi*n/2)/2; a(n)=a(n-1)-a(n-2)+a(n-3). - Paul Barry (pbarry(AT)wit.ie), Aug 30 2004
a(n+2)=sum(b(k), k=0..n), n>=0, with b(k):=A056594(k) (partial sums of S(n, x) Chebyshev polynomials at x=0).
a(n)=-a(n-2)+1, n>=2, a(0)=0=a(1).
G.f.: x^2/((1-x)*(1+x^2))=x^2/(1-x+x^2-x^3).
a(n)=(1/12)*{4*(n mod 4)+[(n+1) mod 4]-2*[(n+2) mod 4]+[(n+3) mod 4]}, with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Oct 23 2007
Contribution from Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Dec 05 2008: (Start)
a(n)=1/2-sin((2n+1)pi/4)/sqrt(2)
a(n)=1/2-cos((2n-1)pi/4)/sqrt(2) (End)
a(n)=(1/4)*[1-(1-I)*I^n-(1+I)*(-I)^n] , with n>=0 and I=sqrt(-1) [From Paolo P. Lava (paoloplava(AT)gmail.com), May 04 2010]
a(n) = floor((n mod 4) / 2). [Reinhard Zumkeller, Apr 15 2011]
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CROSSREFS
| Cf. A062158.
Sequence in context: A091225 A175337 A132380 * A156660 A155899 A117814
Adjacent sequences: A021910 A021911 A021912 * A021914 A021915 A021916
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KEYWORD
| nonn,cons
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Chebyshev comment from W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 10 2004
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