editing

approved

<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 3, 0, -3).

Join[{1, 1}, LinearRecurrence[{0, 3, 0, -3}, {1, 2, 3, 5}, 51]] (* Ray Chandler, Sep 23 2015 *)

approved

editing

editing

approved

G.f.: (2*x^3-x^2-x+1)*(1+x)^2/(1-3*x^2+3*x^4). [From _- _R. J. Mathar_, Jul 17 2009]

A131292 := proc(n) option remember ; if n <= 2 then 1; elif n mod 2 = 1 then 3*(A131292(n-1)-A131292(n-2))+2*A131292(n-3) ; else 3*(A131292(n-1)-A131292(n-2)) ; fi ; end: seq(A131292(n), n=0..80) ; - _# _R. J. Mathar_, Oct 18 2007

Cf. A057083 (bisection). [From _- _R. J. Mathar_, Jul 17 2009]

approved

editing

_Paul Curtz (bpcrtz(AT)free.fr), _, Sep 29 2007

G.f.: (2*x^3-x^2-x+1)*(1+x)^2/(1-3*x^2+3*x^4). [From _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Jul 17 2009]

A131292 := proc(n) option remember ; if n <= 2 then 1; elif n mod 2 = 1 then 3*(A131292(n-1)-A131292(n-2))+2*A131292(n-3) ; else 3*(A131292(n-1)-A131292(n-2)) ; fi ; end: seq(A131292(n), n=0..80) ; - _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Oct 18 2007

Cf. A057083 (bisection). [From _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Jul 17 2009]

More terms from _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Oct 18 2007

G.f.: (2*x^3-x^2-x+1)*(1+x)^2/(1-3*x^2+3*x^4). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 17 2009]

Cf. A057083 (bisection). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 17 2009]

sign,easy,new

Cf. A131665 (0, 0, 1, 3, 6, 11).

sign,easy,new

Sequence is identical to its third differences in absolute value.

sign,easy,new

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

1, 1, 1, 2, 3, 5, 6, 9, 9, 12, 9, 9, 0, -9, -27, -54, -81, -135, -162, -243, -243, -324, -243, -243, 0, 243, 729, 1458, 2187, 3645, 4374, 6561, 6561, 8748, 6561, 6561, 0, -6561, -19683, -39366, -59049, -98415, -118098, -177147, -177147, -236196, -177147, -177147, 0, 177147, 531441, 1062882, 1594323

0,4

Sequence identical to its third differences in absolute value.

A131292 := proc(n) option remember ; if n <= 2 then 1; elif n mod 2 = 1 then 3*(A131292(n-1)-A131292(n-2))+2*A131292(n-3) ; else 3*(A131292(n-1)-A131292(n-2)) ; fi ; end: seq(A131292(n), n=0..80) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 18 2007

Cf. A131665 (0,0,1,3,6,11).

sign,easy,new

Paul Curtz (bpcrtz(AT)free.fr), Sep 29 2007

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 18 2007

approved