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Search: id:A103609
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| 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 5, 5, 8, 8, 13, 13, 21, 21, 34, 34, 55, 55, 89, 89, 144, 144, 233, 233, 377, 377, 610, 610, 987, 987, 1597, 1597, 2584, 2584, 4181, 4181, 6765, 6765, 10946, 10946, 17711, 17711, 28657, 28657, 46368, 46368, 75025, 75025, 121393
(list; graph; listen)
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OFFSET
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0,7
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COMMENT
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The usual policy in the OEIS is not to include such "doubled" sequences. This is an exception. - N. J. A. Sloane (njas(AT)research.att.com).
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FORMULA
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Characteristic polynomial is x^4-x^2-1=0.
a(n) = a(n-2)+a(n-4).
G.f.: x^2(1+x)/(1-x^2-x^4). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 27 2008]
a(n)=(1/5)*[1/2+(1/2)*sqrt(5)]^(1/2)*n*[1/2+(1/2)*sqrt(5)]^[(1/4)*(-1)^n]*[1/2+(1/2)*sqrt(5)]^( -1/4)*sqrt(5)-(1/5)*[1/2-(1/2)*sqrt(5)]^(-1/4)*[1/2-(1/2)*sqrt(5)]^(1/2)*n*[1/2-(1/2) *sqrt(5)]^[(1/4)*(-1)^n]*sqrt(5), with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Oct 06 2008]
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MATHEMATICA
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a[0] = 0; a[1] = 0; a[2] = 1; a[3] = 1; a[n_Integer?Positive] := a[n] = a[n - 2] + a[n - 4]; aa = Table[a[n], {n, 0, 200}]
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PROGRAM
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(Other) sage: taylor( mul((x^2*(1+x))/(1-x^2-x^4) for i in xrange(1, 2)), x, 0, 51)# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 01 2009]
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CROSSREFS
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Partial sums: A094707. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 27 2008]
Sequence in context: A140829 A116575 A090492 this_sequence A129526 A000358 A032244
Adjacent sequences: A103606 A103607 A103608 this_sequence A103610 A103611 A103612
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KEYWORD
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nonn
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Mar 24 2005
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 01 2006
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