0,2

It appears that the sequence coincides with its third order absolute difference. - John W. Layman (layman(AT)math.vt.edu), Sep 05 2003

It appears that, for n>0, the (unsigned) a(n)=3*|A057682(n)|=3*|Sum((-1)^j*binomial(n,3*j+1),j=0..floor(n/3))|. - John W. Layman (layman(AT)math.vt.edu), Sep 05 2003

H. W. Gould, Binomial coefficients, the bracket function, and compositions with relatively prime summands, Fib. Quart. 2 (1964), 241-260.

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

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

a(n)=A007653(3^n).

a(n)=-3a(n-1)-3a(n-2). - Paul Curtz (bpcrtz(AT)free.fr), May 12 2008

a(n)=-(1/2)*I*sqrt(3)*[ -3/2-(1/2)*I*sqrt(3)]^n+(1/2)*I*sqrt(3)*[ -3/2+(1/2)*I *sqrt(3)]^n+(1/2)*[ -3/2+(1/2)*I*sqrt(3)]^n+(1/2)*[ -3/2-(1/2)*I*sqrt(3)]^n, with n>=0 and I=sqrt(-1) - Paolo P. Lava (ppl(AT)spl.at), Jun 11 2008

A000748:=(-1-2*z-3*z**2-3*z**3+18*z**5)/(-1+z+9*z**5); [Conjectured by S. Plouffe in his 1992 dissertation. Gives sequence apart from signs.]

a:= n-> (Matrix ([[ -3, 1], [ -3, 0]])^n)[1, 1]: seq (a(n), n=0..37); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 06 2008]

(PARI) a(n)=if(n<0, 0, polcoeff(1/(1+3*x+3*x^2)+x*O(x^n), n)) /* Michael Somos Jun 07 2005 */

(PARI) {a(n) = if(n<0, 0, 3^((n+1)\2) * (-1)^(n\6) * ((-1)^n + (n%3==2)))} /* Michael Somos Sep 29 2007 */

Cf. A000749, A000750, A001659.

Cf. A057682.

Sequence in context: A021077 A114041 A057083 this_sequence A011383 A007844 A057338

Adjacent sequences: A000745 A000746 A000747 this_sequence A000749 A000750 A000751

sign,easy,eigen

njas