A355021 a(n) = (-1)^n * A000032(n) - 1.

1, -2, 2, -5, 6, -12, 17, -30, 46, -77, 122, -200, 321, -522, 842, -1365, 2206, -3572, 5777, -9350, 15126, -24477, 39602, -64080, 103681, -167762, 271442, -439205, 710646, -1149852, 1860497, -3010350, 4870846, -7881197, 12752042, -20633240, 33385281

Offset

0,2

Comments

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

Closely related (Fibonacci, A000045) partial sums of F(1) - F(2) + F(3) - F(4) + F(5) - ... are given by A355020.

Apart from signs, same as A098600 and A181716.

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).

Formula

a(n) = 2*a(n-2) - a(n-3) for n >= 3. [Corrected by Georg Fischer, Sep 30 2022]

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

Example

a(0) = 1;
a(1) = 1 - 3 = -2;
a(2) = 1 - 3 + 4 = 2;
a(3) = 1 - 3 + 4 - 7 = -5.

Mathematica

f[n_] := Fibonacci[n]; g[n_] := LucasL[n];
f1 = Table[(-1)^n f[n] + 1, {n, 0, 40}]   (* A355020 *)
g1 = Table[(-1)^n g[n] - 1, {n, 0, 40}]   (* this sequence *)
LucasL[-Range[0, 50]] - 1 (* G. C. Greubel, Mar 17 2024 *)
LinearRecurrence[{0, 2, -1}, {1, -2, 2}, 40] (* Harvey P. Dale, Sep 06 2024 *)

Prog

(Magma) [Lucas(-n) -1: n in [0..50]]; // G. C. Greubel, Mar 17 2024
(SageMath) [lucas_number2(-n, 1, -1) -1 for n in range(51)] # G. C. Greubel, Mar 17 2024

Crossrefs

Cf. A000032, A000045, A098600, A181716, A355018, A355019, A355020.

Sequence in context: A356367 A365825 A099926 * A098600 A181716 A261866

Adjacent sequences: A355018 A355019 A355020 * A355022 A355023 A355024

Keyword

sign,easy

Author

Clark Kimberling, Jun 21 2022

Status

approved