#### 15.7.5 Lucas Numbers

`mpz_lucnum2_ui`

derives a pair of Lucas numbers from a pair of Fibonacci
numbers with the following simple formulas.

L[k] = F[k] + 2*F[k-1]
L[k-1] = 2*F[k] - F[k-1]

`mpz_lucnum_ui`

is only interested in *L[n]*, and some work can be
saved. Trailing zero bits on *n* can be handled with a single square
each.

L[2k] = L[k]^2 - 2*(-1)^k

And the lowest 1 bit can be handled with one multiply of a pair of Fibonacci
numbers, similar to what `mpz_fib_ui`

does.

L[2k+1] = 5*F[k-1]*(2*F[k]+F[k-1]) - 4*(-1)^k