Is there a name for (or even the NEED for a name for) taking the starting point (seeding) of Fibonacci's sequence "back" past $0$ or $1$ ?. $$ \left\{\vphantom{A^{A^{A}}}\ldots -21, 13,-8, 5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5, 8, 13, 21\ldots\right\} $$ I figure it could also be rewritten, reversing its order, with subtraction being action as $$ \left\{\vphantom{A^{A^{A}}}\ldots 21, 13, 8, 5, 3, 2, 1, 1, 0, 1, -1, 2, -3, 5, -8, 13, 21\ldots\right\} $$ It seems like someone a lot smarter than me would have already talked about this but it felt pretty good to walk in that person's same footsteps and have those personal "aha!" moments.
Thanks for your time,
Ben Prohm
These are called the Negafibonacci numbers and apparently were introduced by Knuth (see OEIS/A039834).