A130778 Period 6: repeat [1, -1, -3, -3, -1, 1].

1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3

Offset

0,3

Comments

With offset 1, a(n) satisfies the interesting recurrence: a(n+1) = Sum_{k=1..n} binomial(n, k)*(-1)^k*a(k); see Mathematica code below. - John M. Campbell, May 05 2012

Links

Table of n, a(n) for n=0..69.

Index entries for linear recurrences with constant coefficients, signature (2,-2,1).

Formula

From Wesley Ivan Hurt, Jun 19 2016: (Start)

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

a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3) for n>2.

a(n) = (6*cos(n*Pi/3) - 2*sqrt(3)*sin(n*Pi/3) - 3)/3. (End)

Maple

A130778:=n->[1, -1, -3, -3, -1, 1][(n mod 6)+1]: seq(A130778(n), n=0..100); # Wesley Ivan Hurt, Jun 19 2016

Mathematica

Table1 = {1}; a[1] = 1; n = 1; While[n < 314, a[n + 1] = Sum[Binomial[n, k]*(-1)^k*a[k], {k, 1, n}]; AppendTo[Table1, a[n + 1]]; n++]; Print[Table1] (* John M. Campbell, May 05 2012 *)
PadRight[{}, 200, {1, -1, -3, -3, -1, 1}] (* Wesley Ivan Hurt, Jun 19 2016 *)

Prog

(Magma) &cat[[1, -1, -3, -3, -1, 1]^^20]; // Wesley Ivan Hurt, Jun 19 2016

Crossrefs

Sequence in context: A059790 A307156 A326057 * A353516 A351577 A328572

Adjacent sequences: A130775 A130776 A130777 * A130779 A130780 A130781

Keyword

sign,easy

Author

Paul Curtz, Jul 14 2007

Status

approved