alkanes

Originally posted by Acolyte
We can draw any alkane from ethane upwards like this:

...../P'
C-C-Q'
.....\R'

where the Cs are carbon atoms, and P', Q' and R' are collections of carbon atoms (possibly empty) such that P = C-P', Q = C-Q' and R = C-R' are ...[text shortened]... hink of a better representation that deals with this second issue?

I think the "enumeration of alkanes" is a hard problem with no mathematically derivable and absolutely correct solution.

A counting scheme with some duplicates, would be to represent each alkane as an integral number of repeats of the following unit:

.a.
-c-
.b.

where the number of repeates is the order of the alkane, and a and b are alkanes of lesser order. The zeroth alkane is defined as a single hydrogen atom

then the number of alkanes of each order follow the sequence
order1 = 1
order2 = (order1)^4
order3 = ((order2)+(order1))^6
order4 = ((order3)+( order2)+(order1))^8