Let n be the size of alphabet (here 3).

Now ath number in the above scheme will lie between

0 <= a < n or 0 + n <= a < 0 + n + n*n or ...

0 + n + n^2 + ... + n^m <= a < 0 + n + n^2 + ... + n^(m+1)

Solving for m we get,

m = int(log(a(n-1)/n + 1)/log(n))

Here it is,

m = int(log(2*a/3 + 1)/log(3))

Now we subtract n*(n^m-1)/(n-1) from a getting b. b will be a number of (m+1) places in a number system with radix n.

I have put a small python code for it like this:

from math import*

f = lambda a : int(log(2*a/3.0 + 1.0)/ log(3))

alpha = ['a','b','c']


def get_repr(a):
    m = f(a)
    if m == 0:
        b = a
    else:
        trunc = 3*((3**m)-1)/(2)
        b = a - trunc
    s = ''
    for q in range(0, m+1):
        s =   alpha[(b%3)] + s
        b /= 3
    return s


print get_repr(8)

Let n be the size of alphabet (here 3).

Now ath number in the above scheme will lie between

0 <= a < n or 0 + n <= a < 0 + n + n*n or ...

0 + n + n^2 + ... + n^m <= a < 0 + n + n^2 + ... + n^(m+1)

Solving for m we get,

m = int(log(a(n-1)/n + 1)/log(n))

Here it is,

m = int(log(2*a/3 + 1)/log(3))

Now we subtract n*(n^m-1)/(n-1) from a getting b. b will be a number of (m+1) places in a number system with radix n.

I have put a small python code for it like this:

from math import*

f = lambda a : int(log(2*a/3.0 + 1.0)/ log(3))

alpha = ['a','b','c']


def get_repr(a):
    m = f(a)
    if m == 0:
        b = a
    else:
        trunc = 3*((3**m)-1)/(2)
        b = a - trunc
    s = ''
    for q in range(0, m+1):
        s =   alpha[(b%3)] + s
        b /= 3
    return s


print get_repr(8)

EDIT: We can avoid jargon of logarithm and all, and can use the following:

def word(a, alphabet):
    k = 1
    N = len(alphabet)
    n = N
    while True:
        if a < n:
            break
        else:
            a = a - n
            n = n*N
            k = k + 1
    s = ''
    for q in range(0, k):
        s =   alphabet[(a%N)] + s
        a /= N
    return s


print word(1, ['a','b','c'])