A280560 a(n) = (-1)^n * 2 if n!=0, with a(0) = 1.

1, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2

Offset: 0

Author

Michael Somos, Jan 05 2017

Keywords

• sign
• easy

Examples

			G.f. = 1 - 2*x + 2*x^2 - 2*x^3 + 2*x^4 - 2*x^5 + 2*x^6 - 2*x^7 + 2*x^8 - 2*x^9 + ...
		

Links

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

Crossrefs

Cf. A033999, A040000, A084100.

Programs

Magma

[n eq 0 select 1 else 2*(-1)^n: n in [0..75]]; // G. C. Greubel, Jul 29 2018; Mar 28 2024

Mathematica

a[ n_] := (-1)^n (2 - Boole[n == 0]);
PadRight[{1},120,{2,-2}] (* Harvey P. Dale, Jun 04 2019 *)

PARI

{a(n) = (-1)^n * if(n, 2, 1)};

SageMath

[2*(-1)^n -int(n==0) for n in range(76)] # G. C. Greubel, Mar 28 2024

Formula

Euler transform of length 2 sequence [-2, 1].

Moebius transform is length 2 sequence [-2, 4].

a(n) = -2*A033999(n) if n!=0.

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

E.g.f.: 2*exp(-x) - 1.

a(n) = a(-n) for all n in Z.

a(n) = A084100(2*n) = A084100(2*n + 1), if n>=0.

a(n) = (-1)^n * A040000(n).

a(2*n) = A040000(n).

Convolution inverse is A040000.