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Search: id:A133872
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| 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, 1, 0, 0, 1, 1, 0, 0, 1
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Periodic with length 2^2=4.
Partial sums of A056594.
Let i=sqrt(-1) and S(n)=Sum_{k=0..n-1} exp(2*pi*i*k^2/n) for n>=1 the famouse Gauss sum. Then S(n)=(a(n)+a(n+1)*i)*sqrt(n). - Franz Vrabec (franz.vrabec(AT)planetuniqa.at), Nov 08 2007
For any n>=1 the sequence gives the minimum value m>=0 we can get using addition and subtraction among all the numbers from 1 to n. E.g.: n=1 -> m=1; n=2 -> m=2-1=1; n=3 -> m=3-2-1=0; n=4 -> m=4-3-2+1=0; n=5 -> m=5-4+3-2-1=1; n=6 -> m=6+5-4-3-2-1=6-5+4-3-2+1=1; n=7 -> m=7-6+5-4-3+2-1=7+6-5-4-3-2+1=0; etc. - Paolo P. Lava (ppl(AT)spl.at), Feb 29 2008
a(A042948(n)) = 1; a(A042964(n)) = 0. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 03 2008]
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LINKS
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Index entries for characteristic functions
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FORMULA
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a(n)=(1+floor(n/2)) mod 2.
a(n)=A004526(A000035(n+2)).
a(n)=1+floor(n/2)-2*floor((n+2)/4).
a(n)=(((n+2) mod 4)-(n mod 2))/2.
a(n)=((n+2-(n mod 2))/2) mod 2.
a(n)=((2n+3+(-1)^n)/4) mod 2.
a(n)=(1+(-1)^((2n-1+(-1)^n)/4))/2.
a(n)=binomial(n+2,n) mod 2 =binomial(n+2,2) mod 2.
a(n)=A000217(n+1) mod 2.
G.f. g(x)=(1+x)/(1-x^4).
G.f. g(x)=1/((1-x)(1+x^2)).
a(n) = 1/2+(1/2)*cos(Pi*n/2)+(1/2)*sin(Pi*n/2). a(n) = A021913(n+2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 15 2007
a(n)=(1/12)*{-2*(n mod 4)+[(n+1) mod 4]+4*[(n+2) mod 4]+[(n+3) mod 4]}, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Oct 06 2008]
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CROSSREFS
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Cf. A056594. A133620-A133625, A133630, A133633-A133636. A021913. A000217.
Cf. A133882, A133880, A133890, A133900, A133910.
Sequence in context: A125999 A073784 A128130 this_sequence A071026 A068434 A127015
Adjacent sequences: A133869 A133870 A133871 this_sequence A133873 A133874 A133875
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KEYWORD
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nonn
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AUTHOR
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Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Oct 10 2007
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