A355020 a(n) = (-1)^n * A000045(n) + 1.

1, 0, 2, -1, 4, -4, 9, -12, 22, -33, 56, -88, 145, -232, 378, -609, 988, -1596, 2585, -4180, 6766, -10945, 17712, -28656, 46369, -75024, 121394, -196417, 317812, -514228, 832041, -1346268, 2178310, -3524577, 5702888, -9227464, 14930353, -24157816, 39088170

Offset: 0

Author

Clark Kimberling, Jun 21 2022

Keywords

• sign
• easy

Comments

There are the partial sums of F(1) - F(2) + F(3) - F(4) + F(5) - ... .

Closely related (Lucas, A000032) partial sums of L(1) - L(2) + L(3) - L(4) + L(5) - ... are given by A355021.

Apart from signs, same as A008346 and A119282.

Examples

			a(0) = 1;
a(1) = 1 - 1 = 0;
a(2) = 1 - 1 + 2 = 2;
a(3) = 1 - 1 + 2 - 3 = -1.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,2,-1).

Crossrefs

Cf. A000045, A008346, A119282, A355018, A355019, A355021.

Programs

Magma

[1 - Fibonacci(-n): n in [0..50]]; // G. C. Greubel, Mar 17 2024

Mathematica

f[n_] := Fibonacci[n]; g[n_] := LucasL[n];
Table[(-1)^n f[n] + 1, {n, 0, 40}]   (* this sequence *)
Table[(-1)^n g[n] - 1, {n, 0, 40}]   (* A355021 *)
1 - Fibonacci[-Range[0, 50]] (* G. C. Greubel, Mar 17 2024 *)

PARI

a(n) = (-1)^n*fibonacci(n) + 1; \\ Michel Marcus, Jun 24 2022

SageMath

[1 - fibonacci(-n) for n in range(51)] # G. C. Greubel, Mar 17 2024

Formula

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

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