OFFSET
0,3
COMMENTS
a(n) is the product of the n-th and (n+1)th Fibonacci numbers mod the n-th Lucas number.
LINKS
Robert Israel, Table of n, a(n) for n = 0..4761
FORMULA
G.f. (2 + 2*x + 3*x^2 + 7*x^3 + 3*x^4 + 2*x^5 + x^6)*x^2/(1 + x^2 - x^3 - 5*x^4 - 3*x^5 - 2*x^6 - x^7).
For n == 0 (mod 4), a(n) = (A000032(n) - 2)/5.
For n == 1 (mod 4) and n > 1, a(n) = (3*A000032(n) + 2)/5.
For n == 2 (mod 4), a(n) = (4*A000032(n) - 2)/5.
For n == 3 (mod 4), a(n) = (2*A000032(n) + 2)/5.
MAPLE
luc:= n -> combinat:-fibonacci(n+1) + combinat:-fibonacci(n-1):
f:= proc(n) local m;
m:= n mod 4;
if m = 0 then (luc(n)-2)/5
elif m = 1 then (3*luc(n)+2)/5
elif m = 2 then (4*luc(n)-2)/5
else (2*luc(n)+2)/5
fi
end proc:
f(1):= 0:
map(f, [$0..50]);
MATHEMATICA
a[n_] := Mod[Fibonacci[n] * Fibonacci[n + 1], LucasL[n]]; Array[a, 50, 0] (* Amiram Eldar, Oct 03 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Oct 02 2022
STATUS
approved