What is the next term in the sequence 3, 1, -7, 41?

Question

I could detect only one pattern, however, the sign is confusing me

$3 - 1 = 1 \times 2$

$1 - (-7) = 2 \times 2^2$

$-7 - 41 = -3 \times 2^4$

I have a pattern, but I am confused due the to sign.

Answer 1

I would say the next number is

1673

The simple rule:

$n_{i+1} = n_i^2 - 8 $