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

Author

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

Keywords

• easy
• sign

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).

Crossrefs

Cf. A057079.

Programs

Magma

&cat[[1,0,-2,3,-2,0]: n in [0..20]]; // G. C. Greubel, Mar 27 2024

Mathematica

PadRight[{}, 120, {1,0,-2,3,-2,0}] (* 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

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