0,1

a(n)=3a(n-1)-a(n-3)+3a(n-4). - Paul Curtz (bpcrtz(AT)free.fr), Nov 22 2007

a(0)=a(1)=a(2)=-a(3)=-a(4)=-a(5)=1, a(n+6)=a(n) n=0,1.. .

a(n)=(1/3)*{-(n mod 6)+[(n+3) mod 6]}, with n>=0. - Paolo P. Lava (ppl(AT)spl.at), Aug 28 2007

a(n) = ((-1)^n * (4 * (cos((2*n + 1)*Pi/3) + cos(n*Pi)) + 1) - 4) / 3. - Federico Acha Neckar (f0383864(AT)hotmail.com), Sep 01 2007

a(n) = (-1)^n * (4 * cos((2*n + 1) * Pi/3) + 1) / 3. - Federico Acha Neckar (f0383864(AT)hotmail.com), Sep 02 2007

G.f.: (1+x+x^2)/(1+x)/(x^2-x+1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 14 2007

Closed form: a(n)=(1/3)*[1/2-(1/2*I)*sqrt(3)]^n+(1/3)*(-1)^n+(1/3)*[1/2+(1/2*I)*sqrt(3)]^n+[(1/3)*I]*{1/2 -[(1/2)*I]*sqrt(3)}^n*sqrt(3)-[(1/3)*I]*{1/2+[(1/2)*I]*sqrt(3)}^n*sqrt(3), with n>=0 and I=sqrt(-1) - Paolo P. Lava (ppl(AT)spl.at), Jul 17 2008

a(n) = (-1)^floor(n/3). Compare with A057077, A143621 and A143622. Define E(k) = sum {n = 0..inf} a(n)*n^k/n! for k = 0,1,2,... . Then E(k) is an integral linear combination of E(0), E(1) and E(2) (a Dobinski-type relation). Precisely, E(k) = A143628(k) *E(0) + A143629(k) *E(1) + A143630(k) *E(2). [From Peter Bala (pbala(AT)toucansurf.com), Aug 28 2008]

Cf. A131561.

Cf. A131531.

A057077, A143621, A143622, A143628, A143629, A143630. [From Peter Bala (pbala(AT)toucansurf.com), Aug 28 2008]

Sequence in context: A112865 A121241 A122188 this_sequence A143431 A158388 A162285

Adjacent sequences: A130148 A130149 A130150 this_sequence A130152 A130153 A130154

sign

Paul Curtz (bpcrtz(AT)free.fr), Aug 03 2007