OFFSET
0,3
COMMENTS
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 > 2.
G.f.: 1/(1 - 2*x^2 + x^3).
EXAMPLE
a(0) = 1;
a(1) = 1 - 1 = 0;
a(2) = 1 - 1 + 2 = 2;
a(3) = 1 - 1 + 2 - 3 = -1.
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 *)
PROG
(PARI) a(n) = (-1)^n*fibonacci(n) + 1; \\ Michel Marcus, Jun 24 2022
(Magma) [1 - Fibonacci(-n): n in [0..50]]; // G. C. Greubel, Mar 17 2024
(SageMath) [1 - fibonacci(-n) for n in range(51)] # G. C. Greubel, Mar 17 2024
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Clark Kimberling, Jun 21 2022
STATUS
approved