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A010673
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Period 2: repeat [0, 2].
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20
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0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0
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OFFSET
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0,2
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COMMENTS
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Euler number (or Euler characteristic) of (n+1)-sphere. - Franz Vrabec, Sep 07 2007
a(n) = Sum_{k=0..n-1} (-1)^k*N_k, for n >= 1, is Schläfli's generalization of Euler's formula for simply-connected n-dimensional polytopes. N_0 is the number of vertices, ..., N_{d-1} is the number of (d-1)-dimensional faces. See Coxeter's book for references, also for Poincaré's proof. - Wolfdieter Lang, Feb 09 2018
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REFERENCES
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R. Carter, G. Segal, I. Macdonald, Lectures on Lie Groups and Lie Algebras, London Mathematical Society Student Texts 32, Cambridge University Press, 1995; see p. 68.
H. S. M. Coxeter, Regular Polytopes, third ed., Dover publications, New York, 1973, p. 165.
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LINKS
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FORMULA
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a(n) = 1 - (-1)^n.
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MAPLE
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MATHEMATICA
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PadRight[{}, 120, {0, 2}] (* or *) LinearRecurrence[{0, 1}, {0, 2}, 120] (* Harvey P. Dale, May 29 2016 *)
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PROG
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(Maxima) makelist(if evenp(n) then 0 else 2, n, 0, 30); /* Martin Ettl, Nov 11 2012 */
(Maxima) makelist(concat(0, ", ", 2), n, 0, 40); /* Bruno Berselli, Nov 13 2012 */
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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