A079757 Periodic sequence 1, 0, -2, 3, -2, 0, ...

1, 0, -2, 3, -2, 0, 1, 0, -2, 3, -2, 0, 1, 0, -2, 3, -2, 0, 1, 0, -2, 3, -2, 0, 1, 0, -2, 3, -2, 0, 1, 0, -2, 3, -2, 0, 1, 0, -2, 3, -2, 0, 1, 0, -2, 3, -2, 0, 1, 0, -2, 3, -2, 0, 1, 0, -2, 3, -2, 0, 1, 0, -2, 3, -2, 0, 1, 0, -2, 3, -2, 0, 1, 0, -2, 3, -2, 0, 1, 0, -2, 3, -2, 0, 1, 0, -2, 3, -2, 0

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

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

Formula

a(n) = A057079(2*n+1) - (-1)^floor((2*n+1)/2).

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

a(n) = -2*a(n-1) - 2*a(n-2) - a(n-3).

a(n) = |Real(2*(sqrt(3/4)*i - 1/2)^n - (-1)^n )|, where i = sqrt(-1). - Ralf Stephan, Mar 07 2003

Mathematica

PadRight[{}, 120, {1, 0, -2, 3, -2, 0}] (* G. C. Greubel, Mar 27 2024 *)

Prog

(Magma) &cat[[1, 0, -2, 3, -2, 0]: n in [0..20]]; // G. C. Greubel, Mar 27 2024
(SageMath)
def A079757(n): return [1, 0, -2, 3, -2, 0][n%6]
[A079757(n) for n in range(121)] # G. C. Greubel, Mar 27 2024

Crossrefs

Cf. A057079.

Sequence in context: A071484 A372706 A100219 * A071493 A289813 A050075

Adjacent sequences: A079754 A079755 A079756 * A079758 A079759 A079760

Keyword

easy,sign

Author

Mario Catalani (mario.catalani(AT)unito.it), Jan 10 2003

Status

approved