OFFSET
0,4
LINKS
Robert Israel, Table of n, a(n) for n = 0..4761
Index entries for linear recurrences with constant coefficients, signature (-1,3,3,-1,-1).
FORMULA
a(n) = 3 if n >= 3 is odd.
a(n) = A000045(n+2)-3 if n >= 2 is even.
a(n) + a(n+1) - 3*a(n+2) - 3*a(n+3) + a(n+4) + a(n+5) = 0 for n >= 2.
G.f.: -x*(2*x^5-5*x^3-x-1)/((x+1)*(x^2+x-1)*(x^2-x-1)). - Alois P. Heinz, Jan 26 2022
EXAMPLE
a(5) = L(5)*L(6) mod F(7) = 11*18 mod 13 = 3.
MAPLE
F:= combinat:-fibonacci:
L:= n -> F(n-1)+F(n+1):
map(n -> L(n)*L(n+1) mod F(n+2), [$0..30]);
MATHEMATICA
a[n_] := Mod[LucasL[n] * LucasL[n + 1], Fibonacci[n + 2]]; Array[a, 50, 0] (* Amiram Eldar, Jan 26 2022 *)
PROG
(Python)
from gmpy2 import fib, lucas2
def A348591(n): return (lambda x, y:int(x[0]*x[1] % y))(lucas2(n+1), fib(n+2)) # Chai Wah Wu, Jan 26 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
J. M. Bergot and Robert Israel, Jan 25 2022
STATUS
approved