login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A137501 The even numbers repeated, with alternating signs. 5
0, 0, 2, -2, 4, -4, 6, -6, 8, -8, 10, -10, 12, -12, 14, -14, 16, -16, 18, -18, 20, -20, 22, -22, 24, -24, 26, -26, 28, -28, 30, -30, 32, -32, 34, -34, 36, -36, 38, -38, 40, -40, 42, -42, 44, -44, 46, -46, 48, -48, 50, -50, 52, -52, 54, -54, 56, -56, 58, -58, 60, -60, 62, -62, 64, -64, 66, -66, 68, -68, 70, -70, 72, -72, 74 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The general formula for alternating sums of powers of even integers is in terms of the Swiss-Knife polynomials P(n,x) A153641 (P(n,1)-(-1)^k P(n,2k+1))/2. Here n=1 and k shifted one place, thus a(k) = (P(1,1)-(-1)^(k-1) P(1,2(k-1)+1))/2. - Peter Luschny, Jul 12 2009

With just one 0 at the beginning, this is a permutation of all the even integers. - Alonso del Arte, Jun 24 2012

LINKS

Table of n, a(n) for n=0..74.

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

FORMULA

a(n) = ( n - (1/2) + (1/2)*(-1)^n )*(-1)^n

a(n)= -a(n-1) +a(n-2) +a(n-3). G.f.: 2*x^2/((1-x) * (1+x)^2). [From R. J. Mathar, Feb 14 2010]

a(n) = A064455(n) - A123684(n). [Jaroslav Krizek, Mar 22 2011]

MAPLE

den:= n -> (n-1/2+1/2*(-1)^n)*(-1)^n: seq(den(n), n=-10..10);

a := n -> (1+(-1)^n*(2*n-1))/2; [From Peter Luschny, Jul 12 2009]

MATHEMATICA

Flatten[Table[{2n, -2n}, {n, 0, 39}]] (* Alonso del Arte, Jun 24 2012 *)

With[{enos=2*Range[0, 40]}, Riffle[enos, -enos]] (* Harvey P. Dale, Oct 12 2014 *)

CROSSREFS

Cf. A052928.

Sequence in context: A293706 A131055 A052928 * A285999 A005186 A259881

Adjacent sequences:  A137498 A137499 A137500 * A137502 A137503 A137504

KEYWORD

easy,sign

AUTHOR

Carlos Alberto da Costa Filho (cacau_dacosta(AT)hotmail.com), Apr 22 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified June 21 23:05 EDT 2018. Contains 305646 sequences. (Running on oeis4.)