There are many factors to unpack here:
- Fury Cutter's initial base power varying between 10 and 40 depending on which generation you're playing;
- Fury Cutter's base power doubling on each consecutive use until reaching 160;
- Technician's 1.5× boost to base power only applying if the power is <= 60;
- Metronome's boost varying between 1× and 2× depending on the number of consecutive uses;
- Metronome's boost per turn working differently in Gen 4 compared to Gen 5+;
- the order in which each of these boosts apply; and
- the fact that Metronome (and, out of interest, STAB) is not actually a base power modifier.
So we need to be careful with this answer. I'll use DaWoblefet's Damage Dissertation, Smogon's Gen 4 damage formula guide, and Bulbapedia's Metronome and Fury Cutter pages to be as accurate as possible, and break things down by generation.
Since the difference between a BP modifier and a final damage modifier is mostly academic, I'll include calculations with and without Metronome.
DaWoblefet's guide is only up-to-date as of Gen 7, so if there's a similar breakdown available for Gen 8+ then let me know.
Gen 4
Metronome excluded (technically correct)
Turn 1: Fury Cutter (10) × Technician (1.5) = 15 BP
Turn 2: Fury Cutter (20) × Technician (1.5) = 30 BP
Turn 3: Fury Cutter (40) × Technician (1.5) = 60 BP
Turn 4: Fury Cutter (80) × Technician (1) = 80 BP
Turn 5+: Fury Cutter (160) × Technician (1) = 160 BP
Metronome included (what you asked for)
Turn 1: Fury Cutter (10) × Technician (1.5) × Metronome (1) = 15 imaginary BP
Turn 2: Fury Cutter (20) × Technician (1.5) × Metronome (1.1) = 33 imaginary BP
Turn 3: Fury Cutter (40) × Technician (1.5) × Metronome (1.2) = 72 imaginary BP
Turn 4: Fury Cutter (80) × Technician (1) × Metronome (1.3) = 104 imaginary BP
Turn 5: Fury Cutter (160) × Technician (1) × Metronome (1.4) = 224 imaginary BP
Turn 6: Fury Cutter (160) × Technician (1) × Metronome (1.5) = 240 imaginary BP
Turn 7: Fury Cutter (160) × Technician (1) × Metronome (1.6) = 256 imaginary BP
Turn 8: Fury Cutter (160) × Technician (1) × Metronome (1.7) = 272 imaginary BP
Turn 9: Fury Cutter (160) × Technician (1) × Metronome (1.8) = 288 imaginary BP
Turn 10: Fury Cutter (160) × Technician (1) × Metronome (1.9) = 304 imaginary BP
Turn 11+: Fury Cutter (160) × Technician (1) × Metronome (2) = 320 imaginary BP
Gen 5
Metronome excluded (technically correct)
Turn 1: Fury Cutter (20) × Technician (1.5) = 30 BP
Turn 2: Fury Cutter (40) × Technician (1.5) = 60 BP
Turn 3: Fury Cutter (80) × Technician (1) = 80 BP
Turn 4+: Fury Cutter (160) × Technician (1) = 160 BP
Metronome included (what you asked for)
Turn 1: Fury Cutter (20) × Technician (1.5) × Metronome (1) = 30 imaginary BP
Turn 2: Fury Cutter (40) × Technician (1.5) × Metronome (4915/4096) = ~72 imaginary BP
Turn 3: Fury Cutter (80) × Technician (1) × Metronome (5734/4096) = ~128 imaginary BP
Turn 4: Fury Cutter (160) × Technician (1) × Metronome (6553/4096) = ~256 imaginary BP
Turn 5: Fury Cutter (160) × Technician (1) × Metronome (7372/4096) = ~288 imaginary BP
Turn 6+: Fury Cutter (160) × Technician (1) × Metronome (2) = 320 imaginary BP
Gen 6+
Metronome excluded (technically correct)
Turn 1: Fury Cutter (40) × Technician (1.5) = 60 BP
Turn 2: Fury Cutter (80) × Technician (1) = 80 BP
Turn 3+: Fury Cutter (160) × Technician (1) = 160 BP
Metronome included (what you asked for)
Turn 1: Fury Cutter (40) × Technician (1.5) × Metronome (1) = 60 imaginary BP
Turn 2: Fury Cutter (80) × Technician (1) × Metronome (4915/4096) = ~96 imaginary BP
Turn 3: Fury Cutter (160) × Technician (1) × Metronome (5734/4096) = ~224 imaginary BP
Turn 4: Fury Cutter (160) × Technician (1) × Metronome (6553/4096) = ~256 imaginary BP
Turn 5: Fury Cutter (160) × Technician (1) × Metronome (7372/4096) = ~288 imaginary BP
Turn 6+: Fury Cutter (160) × Technician (1) × Metronome (2) = 320 imaginary BP
If you want to include STAB as well, then put a 1.5× boost on everything above (STAB kicks in after Technician and before Metronome in all games).
As you can see, this strategy takes a long time to do respectable damage, offers no immediate firepower, and consumes your item slot. Not viable in competitive.