0,3

Euler transform of finite sequence [2,-2,0,1]. - Michael Somos Sep 17 2004

This is the r=2 member in the r-family of sequences S_r(n) defined in A092184 where more information can be found.

A007877(n+1) is the transform of sqrt(1+2x)/sqrt(1-2x) (A063886) under the Chebyshev transformation A(x)->(1/(1+x^2))A(x/(1+x^2)). See also A084099. - Paul Barry (pbarry(AT)wit.ie), Oct 12 2004

Multiplicative with a(2) = 2, a(2^e) = 0 if e >= 2, a(p^e) = 1 otherwise. David W. Wilson (davidwwilson(AT)comcast.net) Jun 12, 2005.

Index entries for sequences related to Chebyshev polynomials.

Multiplicative with a(p^e) = 2 if p = 2 and e = 0; 0 if p = 2 and e > 0; 1 if p > 2. - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001.

a(n)=-sum{k=0..n, (-1)^C(k+2, 2)} (Offset -1) - Paul Barry (pbarry(AT)wit.ie), Jul 07 2003

a(n)=1-cos(n*pi/2) a(n)=a(n-1)-a(n-2)+a(n-3) - Lee Reeves (leereeves(AT)fastmail.fm), May 10 2004

a(n)= -a(n-2)+2, n>=2, a(0)=0, a(1)=1.

a(n)= a(n-1)-a(n-2)+a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=2.

G.f.: x*(1+x)/((1-x)*(1+x^2))=x*(1+x)/(1-x+x^2-x^3).

a(n)=1-T(n, 0)= 1-A056594(n) with Chebyshev's polynomials T(n, x) of the first kind. Note that T(n, 0)=S(n, 0).

a(n)= b(n) + b(n-1), n>=1, with b(n):=A021913(n+1) the partial sums of S(n, 0)= U(n, 0)=A056594(n)(Chebyshev's polynomials evaluated at x=0).

1 + (1/2){(-1)^[(n-1)/2] - (-1)^[n/2] }. - Ralf Stephan, Jun 09 2005

a(n)=1/12*{5*(n mod 4)+5*[(n+1) mod 4]-[(n+2) mod 4]-[(n+3) mod 4]} - Paolo P. Lava (ppl(AT)spl.at), Oct 20 2006

Sequence in context: A090787 A096661 A098178 this_sequence A118825 A118822 A054848

Adjacent sequences: A007874 A007875 A007876 this_sequence A007878 A007879 A007880

nonn,easy,mult

Christopher Lam Cham Kee (Topher(AT)CyberDude.Com)

Chebyshev comments from W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 10 2004