The following is an attempt to combine elements of the neohaiku and the Fibonacci Haiku. I know this all started out as a joke, but then I got all caught up in the mathematical puzzles of it, and ended up producing the most pretentious lyrical artform since "Your mom"jokes. I apologize dishonestly.
Okay. So! The elusive Fibonaccineohaiku! I have scribbled and struggled with a bit of math on my end, and I think I might have something interesting.
My idea is a poem consisting of 3 textblocks, or verses, each line in each verse containing an amount of syllables equal to a fibonaccinumber, (where MaxClimb's, was a combination of Fibonacci and Primenumbers.).
I'm thinking that any given line will contain either the fibonaccinumber directly above or below the one in the line before. (This provides some wriggleroom, against the straitjacket that is the rest of the rules).
Now; the first and third verse must be of equal length (Just to keep the haikuthing going), and shorter than the middle one. Forget about the 1.4sizeratio. It isn't practiceable, when you take into account that:
Every verse must have a total number of syllables equal to a primenumber, and the poems total number of syllables must be so too
For added coolness you can mirror the first and third verse (See below).
maxClimb suggests that you should always have the center line of the second verse be the next sequential Fibonaccinumber from the one that ended the first verse. Of course this adds difficulty. But there are no strict rules here, just a big, benign brainstorm.
Ain't that something? I made a representation of how this could look:
First verse:
0 = 33 syllables (Prime)
1
1
2
3
5
8
13

Second.
2 = 61 syllables (Prime)
1
1
0
1
1
2
3
5
8
13
8
5
3
2
1
1
0
1
1
2

Third.
13 = 33 (Prime)
8
5
3
2
1
1
0
Complete total: 127 syllables ! (Prime) !
There should be loads of other ways to make it all fit, though. It just takes some time and a bit of
figuring out.
Fun fact: If you take a normal haiku it goes
5 : 7 : 5  meaning each
verse has a prime number of syllables and also:
5 + 7 + 5 = 17. The total number of syllables is a prime number.
Some of you probably already read the
heartbreaking tragedy of my pet clam,
Rufus when I used it in my
Neohaiku writeup. Just to demonstrate how easily a normal haiku can be
transformed into a Fibonaccineohaiku, here it is again, in it's original form, and as a FNHaiku
My pet clam is sad
So much work to no avail
the pearl now lies crushed
As a fibonacci neohaiku could go:
My

pet
Clam
is sad

so
much
work to
no avail
the pearl
now
lies

crushed
As you've probably noticed I use "" to denote zeroes in the Fibonacci sequence.
Below this is my first try at actually making one, and not just the concept of one. I'm afraid I should have stuck to the conceptual stuff.
The Bard on the Mountaintop
A FibonaccineoHaiku
<
Clouds,
Wyrms,
beneath.
Fire they breathe.
Fight eternal wars,
snack on a horse, or sometimes worse.
So I go where they cannot, run to my cave, my hut.
Sit down
in
chair.

I
flip
the switch
and they stare.
Jealously at me,
and my bigass Plasma TV.
Yes, they'd much rather be watching a rerun on Fox
figthing, flying, burning  it sucks!
I tell them: "Bring me
Projector"
"For a
screen
we'll

use
a
Glacier."
Now I'm Dragon King, ruling my land through fear, and fire
Gotta run down to Blockbuster
tonight we're watching
"Streetcar named
Desire"
A
gain

If you have not interested yourself in our recent haiku craze, I suggest checking out maxClimbs Fibonacci Haiku, my own NeoHaiku and maats Librivoxwriteup.
Or even just the Haiku node, if you are unaware of what a haiku is.
My roommate says the best thing about these is the way you end up sounding like GlaDOS when you recite them...
By the way, loads of creds go to maxClimb, Dimview, maat and other people who have helped this strange idea take on the epically weird and large proportions it has achieved.
Everyone and their mother have written to inform me that 33 is not a primenumber. I recognize this irrefutable truth. Some of you may ask yourselves: "Did you mindlessly get your primes from some list of such, on teh interwebz, without checking their validity?"
the answer would be yes. Yes I did.