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A355021 a(n) = (-1)^n * L(n) - 1, where L = A000032 (Lucas numbers). 4
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..36.

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

FORMULA

a(n) = 2*a(n-1) + a(n-2) for n >= 2.

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}]   (* A355021 *)

CROSSREFS

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

Sequence in context: A335240 A099926 A181716 * A098600 A261866 A147766

Adjacent sequences:  A355018 A355019 A355020 * A355022 A355023 A355024

KEYWORD

sign,easy

AUTHOR

Clark Kimberling, Jun 21 2022

STATUS

approved

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Last modified September 25 12:12 EDT 2022. Contains 356984 sequences. (Running on oeis4.)