login
A348592
a(n) = F(n)*F(n+1) mod L(n+2) where F=A000045 is the Fibonacci numbers and L = A000032 is the Lucas numbers.
2
0, 1, 2, 6, 15, 11, 10, 45, 99, 79, 65, 312, 675, 545, 442, 2142, 4623, 3739, 3026, 14685, 31683, 25631, 20737, 100656, 217155, 175681, 142130, 689910, 1488399, 1204139, 974170, 4728717, 10201635, 8253295, 6677057, 32411112, 69923043, 56568929, 45765226, 222149070, 479259663, 387729211, 313679522
OFFSET
0,3
FORMULA
For n >= 1, a(n) = (A070352(n+2)*A000032(n+2) + 3*(-1)^n)/5.
a(n) + 2*a(n + 1) + 3*a(n + 2) + 5*a(n + 3) + a(n + 4) - a(n + 5) - a(n + 7) = 0 for n >= 1.
G.f.: -3 + 3/(5*(1+x)) + (3+x)/(2*(1-x-x^2)) + (9-4*x+6*x^2-x^3)/(10*(1+3*x^2+x^4)).
EXAMPLE
a(5) = F(5)*F(6) mod L(7) = 5*8 mod 29 = 11.
MAPLE
F:= combinat:-fibonacci:
L:= n -> F(n-1)+F(n+1):
seq(F(n)*F(n+1) mod L(n+2), n=0..20);
MATHEMATICA
a[n_] := Mod[Fibonacci[n] * Fibonacci[n + 1], LucasL[n + 2]]; Array[a, 50, 0] (* Amiram Eldar, Jan 26 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
J. M. Bergot and Robert Israel, Jan 25 2022
STATUS
approved