Find the number of occurrences of a subsequence in a string

Question

For example, let the string be the first 10 digits of pi, 3141592653, and the subsequence be 123. Note that the sequence occurs twice:

Answer 1

My quick attempt:

def count_subseqs(string, subseq):
    string = [c for c in string if c in subseq]
    count = i = 0
    for c in string:
        if c == subseq[0]:
            pos = 1
            for c2 in string[i+1:]:
                if c2 == subseq[pos]:
                    pos += 1
                    if pos == len(subseq):
                        count += 1
                        break
        i += 1
    return count

print count_subseqs(string='3141592653', subseq='123')

Edit: This one should be correct also if 1223 == 2 and more complicated cases:

def count_subseqs(string, subseq):
    string = [c for c in string if c in subseq]
    i = 0
    seqs = []
    for c in string:
        if c == subseq[0]:
            pos = 1
            seq = [1]
            for c2 in string[i + 1:]:
                if pos > len(subseq):
                    break
                if pos < len(subseq) and c2 == subseq[pos]:
                    try:
                        seq[pos] += 1
                    except IndexError:
                        seq.append(1)
                        pos += 1
                elif pos > 1 and c2 == subseq[pos - 1]:
                    seq[pos - 1] += 1
            if len(seq) == len(subseq):
                seqs.append(seq)
        i += 1
    return sum(reduce(lambda x, y: x * y, seq) for seq in seqs)

assert count_subseqs(string='12', subseq='123') == 0
assert count_subseqs(string='1002', subseq='123') == 0
assert count_subseqs(string='0123', subseq='123') == 1
assert count_subseqs(string='0123', subseq='1230') == 0
assert count_subseqs(string='1223', subseq='123') == 2
assert count_subseqs(string='12223', subseq='123') == 3
assert count_subseqs(string='121323', subseq='123') == 3
assert count_subseqs(string='12233', subseq='123') == 4
assert count_subseqs(string='0123134', subseq='1234') == 2
assert count_subseqs(string='1221323', subseq='123') == 5