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A105385
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Expansion of (1-x^2)/(1-x^5).
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1
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1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1
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OFFSET
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0,1
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COMMENTS
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Binomial transform is A103311(n+1). Consecutive pair sums of A105384. Periodic {1,0,-1,0,0}.
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LINKS
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Table of n, a(n) for n=0..90.
Index to sequences with linear recurrences with constant coefficients, signature (-1,-1,-1,-1).
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FORMULA
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G.f.: (1+x)/(1+x+x^2+x^3+x^4); a(n)=sqrt(1/5-2sqrt(5)/25)cos(4*pi*n/5+pi/10)+sqrt(5)sin(4*pi*n/5+pi/10)/5+ sqrt(2sqrt(5)/25+1/5)cos(2*pi*n/5+3*pi/10)+sqrt(5)sin(2*pi*n/5+3*pi/10)/5
a(n)=-(1/5)*{[n mod 5]+[(n+2) mod 5]-[(n+3) mod 5]-[(n+4) mod 5]}, with n>=0. - Paolo P. Lava, Jun 01 2007
a(n)=A092202(n+1). [From R. J. Mathar, Aug 28 2008]
a(0)=1, a(1)=0, a(2)=-1, a(3)=0, a(n)=a(n-1)-a(n-2)-a(n-3)-a(n-4). - Harvey P. Dale, Mar 10 2013
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MATHEMATICA
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CoefficientList[Series[(1-x^2)/(1-x^5), {x, 0, 100}], x] (* or *) PadRight[{}, 100, {1, 0, -1, 0, 0}] (* or *) LinearRecurrence[{-1, -1, -1, -1}, {1, 0, -1, 0}, 100] (* Harvey P. Dale, Mar 10 2013 *)
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CROSSREFS
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Cf. A198517 (unsigned version).
Sequence in context: A127829 A127831 A164364 * A090626 A129569 A030658
Adjacent sequences: A105382 A105383 A105384 * A105386 A105387 A105388
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KEYWORD
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sign,easy
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AUTHOR
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Paul Barry, Apr 02 2005
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STATUS
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approved
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