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Search: id:A133882
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| A133882 |
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Binomial(n+2,n) mod 2^2. |
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+0
5
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| 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Periodic with length 2^3=8.
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FORMULA
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a(n)=binomial(n+2,2) mod 2^2.
G.f. g(x)=(1+3x+2x^2+2x^3+3x^4+x^5)/(1-x^8).
G.f. g(x)=(1+x)(1+2x+2x^3+x^4)/(1-x^8)=(1+2x+2x^3+x^4)/((1-x)(1+x^2)(1+x^4))
a(n)=A105198(n+1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 08 2008
a(n)=(1/56)*{-4*(n mod 8)+3*[(n+1) mod 8]+10*[(n+2) mod 8]+17*[(n+3) mod 8]-4*[(n+4) mod 8]+3*[(n+5) mod 8]+10*[(n+6) mod 8]-11*[(n+7) mod 8]}, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Oct 06 2008]
a(n)=1.5 + 0*( - 1)^n - 0.5*cos(Pi*n/4) + (1/2 + 1/2*2^(1/2))*sin(Pi*n/4) - 0.5*cos(3*Pi*n/4) + ( - 1/2 + 1/2*2^(1/2))*sin(3*Pi*n/4) + 0.5*cos(n*Pi/2) + 0.5*sin(n*Pi/2) [From Richard Choulet (richardchoulet(AT)yahoo.fr), Dec 12 2008]
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CROSSREFS
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Cf. A000040, A133620-A133625, A133630, A133633-A133636.
Cf. A133872, A133880, A133890, A133900, A133910.
For the sequence regarding "binomial(n+2, n) mod 2" see A133872.
Sequence in context: A073756 A006379 A105198 this_sequence A092106 A052901 A127807
Adjacent sequences: A133879 A133880 A133881 this_sequence A133883 A133884 A133885
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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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