0,2

Inverse binomial transform of A057083. Binomial transform of A061347. The sums of consecutive pairs of elements give A084103. - Paul Barry (pbarry(AT)wit.ie), May 15 2003

Hexaperiodic sequence identical to its third differences. - Paul Curtz (bpcrtz(AT)free.fr), Dec 13 2007

a(n+1) is the Hankel transform of A001700(n+1)-A001700(n). [From Paul Barry (pbarry(AT)wit.ie), Apr 21 2009]

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)

Index entries for sequences related to Chebyshev polynomials.

a(n)=S(n, 1)+S(n-1, 1) = S(2*n, sqrt(3)); S(n, x) := U(n, x/2), Chebyshev polynomials of 2nd kind, A049310. S(n, 1)= A010892(n).

a(n) =2*cos((n-1)*pi/3) =a(n-1)-a(n-2) =-a(n-3) =a(n-6) =(A022003(n+1)+1)*(-1)^[n/3]. Unsigned a(n) =4-a(n-1)-a(n-2) - Henry Bottomley (se16(AT)btinternet.com), Mar 29 2001

a(n)=(-1)^Floor[n/3]+((-1)^Floor[(n-1)/3]+(-1)^Floor[(n+1)/3])/2 - Mario Catalani (mario.catalani(AT)unito.it), Jan 07 2003

a(n)=(1/2-sqrt(3)i/2)^(n-1)+(1/2+sqrt(3)i/2)^(n-1)=cos(pi*n/3)+sqrt(3)sin(pi*n/3) - Paul Barry (pbarry(AT)wit.ie), Mar 15 2004

The period 3 sequence (2, -1, -1, ...) has a(n)=2cos(2pi*n/3)=(-1/2-sqrt(3)i/2)^n+(-1/2+sqrt(3)i/2)^n - Paul Barry (pbarry(AT)wit.ie), Mar 15 2004

Euler transform of length 6 sequence [ 2, -2, -1, 0, 0, 1]. - Michael Somos Jul 14 2006

G.f.: (1+x)/(1-x+x^2) = (1-x^2)^2*(1-x^3)/((1-x)^2*(1-x^6)) . a(2-n)==a(n) . - Michael Somos Jul 14 2006

a(n)=-1/6*{2*(n mod 6)+[(n+1) mod 6]-[(n+2) mod 6]-2*[(n+3) mod 6]-[(n+4) mod 6]+[(n+5) mod 6]} with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Nov 20 2006

a(n)=A033999(A002264(n))*(A000035(A010872(n))+1). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 20 2007

a(n)=(3*A033999(A002264(n))-A033999(n))/2. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 20 2007

a(n)=(-1)^floor(n/3)*((n mod 3) mod 2 + 1). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 20 2007

a(n)=(3*(-1)^floor(n/3)-(-1)^n)/2. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 20 2007

(PARI) a(n)=[1, 2, 1, -1, -2, -1][n%6+1] /* Michael Somos Jul 14 2006 */

(PARI) {a(n)=if(n<0, n=2-n); polcoeff((1+x)/(1-x+x^2)+x*O(x^n), n)} /* Michael Somos Jul 14 2006 */

A049310, A010892. Apart from signs, same as A061347.

Cf. A061347.

a(n)=A010892(n)+A010892(n-1)

Cf. A002264, A010872.

Sequence in context: A107751 A132367 A101825 this_sequence A087204 A131534 A061347

Adjacent sequences: A057076 A057077 A057078 this_sequence A057080 A057081 A057082

easy,sign

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 04 2000