Aromatic rings have 4n+2 pi electrons, where n is any integer. You don't see odd numbers of carbons in aromatic rings too often because the pattern of alternating double bonds is disrupted - if you have a cation or anion, though, odd-numbered aromatics are possible.
Tropylium cation is one such aromatic ring - same pi electron count as benzene, but one extra carbon. The ion is so stable you can actually isolate tropylium fluoborate (not sure about other counterions). It is also an ubiquitous peak in EI mass spec from alkylbenzenes.
Analogously, complexes of cyclopentadienyl anion are known (the famous "sandwich organometallics" like ferrocene). n can also equal zero - even cyclopropenium is known!
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"where pi is any integer."
You might want to double-check that one ;)
But then again we all know that in Alaska Pi is only 3.00 because everything shrinks in the cold. They call it Eskimo Pi.
It didn't catch on in Indiana.
The joys of trying to teach organic chem to some.
"For a ring to be aromatic it needs to be cyclic and conjugated with 4n + 2 pi electrons"
"So that means benzene has -0.0708 electrons?"
CAS search discloses a substantial majority of all catalogued discreet organics possess 2n carbons. A notable exception is cholesterol (C27 H46 O) biosynthesized from acetate units and then edited.
1800s' tropylium syntheses were deep-sixed by organic product unexpectedly entering the aqueous phase then down the drain. Ferrocene was corrosion in a petroleum refinery fractionating tower insubordinately retrieved and examined by a chemist where only engineers should hold sway. And so it goes - all discovery is insubordinate.
Tetraphenylcyclopentadienone owes its marvelous color and large epsilon to its formally anti-aromatic ring - the carbonyl carbon has a cationic resonance contributor.