OFFSET
1,2
COMMENTS
By definition, the arithmetic mean of a(1), ... a(n) is equal to L(n) and a(n) - Lucas(n) = (n - 1) * Lucas(n - 2). See A136391 for the Fibonacci case.
FORMULA
EXAMPLE
a(6) = 53 = 6*Lucas(6) - 5*Lucas(5) = 6 * 18 - 5 * 11 = 108 - 55.
a(4) = 16 = 4*Lucas(2) + Lucas(3) = 3*Lucas(2) + Lucas(4).
MAPLE
with(combinat): seq(n*(fibonacci(n-1)+fibonacci(n-3)) +fibonacci(n)+fibonacci(n-2), n=1..40).
MATHEMATICA
Table[LucasL[n]n - LucasL[n - 1](n - 1), {n, 35}] (* Alonso del Arte, Sep 02 2014 *)
PROG
(PARI) a(n) = n*(fibonacci(n-1)+fibonacci(n-3)) +fibonacci(n)+fibonacci(n-2); \\ Michel Marcus, Sep 02 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Giuseppe Coppoletta, Sep 02 2014
STATUS
approved