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Search: id:A078070
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| A078070 |
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Expansion of (1-x)/(1+2*x+2*x^2+x^3). |
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+0
3
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| 1, -3, 4, -3, 1, 0, 1, -3, 4, -3, 1, 0, 1, -3, 4, -3, 1, 0, 1, -3, 4, -3, 1, 0, 1, -3, 4, -3, 1, 0, 1, -3, 4, -3, 1, 0, 1, -3, 4, -3, 1, 0, 1, -3, 4, -3, 1, 0, 1, -3, 4, -3, 1, 0, 1, -3, 4, -3, 1, 0, 1, -3, 4, -3, 1, 0, 1, -3, 4, -3, 1, 0, 1, -3, 4, -3, 1, 0, 1, -3
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Euler transform of finite sequence [ -3,1,1]. - Michael Somos Sep 17 2004
The unsigned sequence is the r=3 member in the r-family of sequences S_r(n) defined in A092184 where more information can be found. |a(n)|= 2-2*T(n,1/2), with twice the Chebyshev's polynomials of the first kind 2*T(n,x=1/2)= A057079(n+1)= S(n+1,1)+S(n,1) with S(n,1)= A010892(n).
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LINKS
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Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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abs(a(n))=2+2cos(pi*n/3-2pi/3). - Paul Barry (pbarry(AT)wit.ie), Mar 14 2004
a(n)=(n+1)sum{k=0..floor((n+1)/2), (-1)^k*binomial(n-k+1, k)*(-1)^(n-2k+1)/(n-k+1)}+2*(-1)^n; a(n)=2T(n+1, -1/2)+2(-1)^n. - Paul Barry (pbarry(AT)wit.ie), Dec 12 2004
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CROSSREFS
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Sequence in context: A072681 A064460 A108481 this_sequence A111028 A096646 A136206
Adjacent sequences: A078067 A078068 A078069 this_sequence A078071 A078072 A078073
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 17 2002
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EXTENSIONS
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Chebyshev comment and related formulas from W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 10 2004
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