Paraffins

Paraffins is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

The purpose of this task is to count how many different paraffin molecules there are for a given number of carbon atoms. The molecules must be topologically different, so all reflections, etc. are counted once.

The input is just the number 'n' of carbon atoms of a molecule, like 17.

The output is how many different different paraffins there are with 'n' carbon atoms (like 24_894 if n = 17).

The sequence of those results can be seen in the Sloane encyclopedia.

The sequence is (the index starts from 1, and represents the number of carbon atoms):

1, 1, 1, 1, 2, 3, 5, 9, 18, 35, 75, 159, 355, 802, 1858, 4347, 10359, 24894, 60523, 148284, 366319,
910726, 2278658, 5731580, 14490245, 36797588, 93839412, 240215803, 617105614, 1590507121, 4111846763,
10660307791, 27711253769, ...

Extra credit: show the paraffins in some way. A flat 1D representation, with arrays or lists is enough, like:

<lang haskell>

• Main> all_paraffins 1

[CCP H H H H]

• Main> all_paraffins 2

[BCP (C H H H) (C H H H)]

• Main> all_paraffins 3

[CCP H H (C H H H) (C H H H)]

• Main> all_paraffins 4

[BCP (C H H (C H H H)) (C H H (C H H H)),CCP H (C H H H) (C H H H)
(C H H H)]

• Main> all_paraffins 5

[CCP H H (C H H (C H H H)) (C H H (C H H H)),CCP H (C H H H) (C H H H)
(C H H (C H H H)),CCP (C H H H) (C H H H) (C H H H) (C H H H)]

• Main> all_paraffins 6

[BCP (C H H (C H H (C H H H))) (C H H (C H H (C H H H))),BCP (C H H
(C H H (C H H H))) (C H (C H H H) (C H H H)),BCP (C H (C H H H)
(C H H H)) (C H (C H H H) (C H H H)),CCP H (C H H H) (C H H
(C H H H)) (C H H (C H H H)),CCP (C H H H) (C H H H) (C H H H)
(C H H (C H H H))]

</lang>

Showing a basic 2D ASCII-art representation of the molecules is even better.

A Scheme implementation: http://www.ccs.neu.edu/home/will/Twobit/src/paraffins.scm

A Haskell implementation: http://darcs.brianweb.net/nofib/imaginary/paraffins/Main.hs

An old paper that explains the functional code, with some molecules shown too: http://www.cs.wright.edu/~tkprasad/courses/cs776/paraffins-turner.pdf

There is a Fortress implementation too (turnersParaffins0.fss).