OFFSET
1,2
COMMENTS
Consider the sum of the 4*n Lucas numbers from index 1 through 4*n. It is divisible by the (n+1)st Lucas number and the ratio is 5*a(n).
LINKS
Index entries for linear recurrences with constant coefficients, signature (3,6,-3,-1).
FORMULA
G.f.: x*(1 + 3*x)/((1 + x - x^2)*(1 - 4*x - x^2)). - Stefano Spezia, May 20 2024
EXAMPLE
a(3) = Fibonacci(4)*Fibonacci(6) = 3*8 = 24. The sum of the first 12 Lucas numbers is 840, which is the 4th Lucas number (7) times 5*a(3).
MATHEMATICA
Table[Fibonacci[k + 1] Fibonacci[2 k], {k, 30}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Tanya Khovanova and the MIT PRIMES STEP senior group, May 18 2024
STATUS
approved