|
| |
|
|
A137501
|
|
The even numbers repeated and with the sign changed.
|
|
3
| |
|
|
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; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Contribution from Peter Luschny (peter(AT)luschny.de), Jul 12 2009: (Start)
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. (End)
|
|
|
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 (mathar(AT)strw.leidenuniv.nl), 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 (peter(AT)luschny.de), Jul 12 2009]
|
|
|
CROSSREFS
| Cf. A052928.
Sequence in context: A161764 A131055 A052928 * A005186 A008642 A001364
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
|
| |
|
|
