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A010673 Period 2: repeat [0, 2]. 16
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Euler number (or Euler characteristic) of (n+1)-sphere. - Franz Vrabec, Sep 07 2007

First differences of A109613. - Reinhard Zumkeller, Dec 05 2009

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

REFERENCES

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.

LINKS

Muniru A Asiru, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,1)

FORMULA

a(n) = 1 - (-1)^n.

a(n) = 2*(n mod 2). - Paolo P. Lava, Oct 20 2006

G.f.: -2*x / ((x-1)*(1+x)). - R. J. Mathar, Apr 06 2011

MAPLE

seq(op([0, 2]), n=0..80); # Muniru A Asiru, Oct 26 2018

MATHEMATICA

PadRight[{}, 120, {0, 2}] (* or *) LinearRecurrence[{0, 1}, {0, 2}, 120] (* Harvey P. Dale, May 29 2016 *)

PROG

(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 */

(PARI) a(n)=1-(-1)^n \\ Charles R Greathouse IV, Oct 07 2015

(GAP) Flat(List([0..80], n->[0, 2])); # Muniru A Asiru, Oct 26 2018

CROSSREFS

Sequence in context: A267602 A021499 A176742 * A084099 A036665 A053472

Adjacent sequences:  A010670 A010671 A010672 * A010674 A010675 A010676

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 23 11:44 EDT 2019. Contains 325254 sequences. (Running on oeis4.)