Greetings all,
I would use a hash and a for loop... 
#!/usr/bin/perl -w
use strict;
use Dumpvalue;

my $d = new Dumpvalue;
my %count;

my $DNAstr = <DATA>;
chomp($DNAstr);

my @bases = split //, $DNAstr;

for(my $i = 0 ; $i < scalar(@bases); $i++){
    $count{$bases[$i]}++;
    $count{$bases[$i].$bases[$i+1]}++ if(defined $bases[$i+1]);
    $count{$bases[$i].$bases[$i+1].$bases[$i+2]}++ if(defined $bases[$
+i+2]);
}

$d->dumpValues(\%count);

[download]
Here is the data I was using. 
__DATA__
AGATAGCGCTGATCGAGAGCTATAGCGATCGATCGGATCGATCGGGATCTTAGCGAAAAGCTCGAT
TTAGCTAGCTAAAAAAAAAATTTTTTGGGGGCGAGATCGATCGATCGATCGCGCTTAGGAAATTCC
CCCGCGCGCGGCCCCCGAGATAGGGATAGGATAGGGATAGAGATCGCGCTAGCTCGATCGCGCGCT
AGATTATATATATATTAGCGGCGCGATAGCTCGCTAGCTGCTAGCTCGCTAGCTCGATCTTCTCGA
TCGCGGCTAGGAGAGCTCGAGCTTCGAGGCTGCGAGGATCGCGGAGAGGAGGATCGAGATCGGATA
GAGATCGCGCTAGCTCGATCGCGCGCTAGATTATATATATATTAGCGGCGCGATAGCTCGCTAGCT
GCTAGCTCGCTAGCTCGATCTTCTCGATCGCGGCTAGGAGAGCTCGAGCTTCGAGGCTGCGAGGAT
CGCGGAGAGGAGGATCGAGATCGGATCGAGAGCTATAGCGATCGATCGGATCGATCGGGATCTTAG
CGAAAAGCTCGATTTAGCTAGCTAAAAAAAAAATTTTTTGGGGGCGAGATCGATCGATCGATCGCG
CTTAGGAAATTCCCCCGCGCGCGGCCCCCGAGATAGGGATAGGATAGGGATAGAGATCGCGCTAGC
TCGATCGCGCGCTAGATTATATATATATTAGCGGCGCGATAGCTCGCTAGCTGCTAGCTCGCTAGC
TCGATCTTCTGATAGCGCTGATCGAGAGCTATAGCGATCGATCGGATCGATCGGGATCTTAGCGAA
AAGCTCGATTTAGCTAGCTAAAAAAAAAATTTTTTGGGGGCGAGATCGATCGATCGATCGCGCTTA
GGAAATTCCCCCGCGCGCGGCCCCCGAGATAGGGATAGGATAGGGATAGAGATCGCGCTAGCTCGA
TCGCGCGCTAGATTATATATATATTAGCGGCGCGATAGCTCGCTAGCTGCTAGCTCGCTAGCTCGA
TCTTCTCGATCGCGGCTAGGAGAGCTCGAGCTTCGAGGCTGCGAGGATCGCGGAGAGGAGGATCGA
GATCGGATAGAGATCGCGCTAGCTCGATCGCGCGCTAGATTATATATATATTAGCGGCGCGATAGC
TCGCTAGCTGCTAGCTCGCTAGCTCGATCTTCTCGATCGCGGCTAGGAGAGCTCGAGCTTCGAGGC
TGCGAGGATCGCGGAGAGGAGGATCGAGATCGGATCGAGAGCTATAGCGATCGATCGGATCGATCG
GGATCTTAGCGAAAAGCTCGATTTAGCTAGCTAAAAAAAAAATTTTTTGGGGGCGAGATCGATCGA
TCGATCGCGCTTAGGAAATTCCCCCGCGCGCGGCCCCCGAGATAGGGATAGGATAGGGATAGAGAT
CGCGCTAGCTCGATCGCGCGCTAGATTATATATATATTAGCGGCGCGATAGCTCGCTAGCTGCTAG
CTCGCTAGCTCGATCTTCGATAGCGCTGATCGAGAGCTATAGCGATCGATCGGATCGATCGGGATC
TTAGCGAAAAGCTCGATTTAGCTAGCTAAAAAAAAAATTTTTTGGGGGCGAGATCGATCGATCGAT
CGCGCTTAGGAAATTCCCCCGCGCGCGGCCCCCGAGATAGGGATAGGATAGGGATAGAGATCGCGC
TAGCTCGATCGCGCGCTAGATTATATATATATTAGCGGCGCGATAGCTCGCTAGCTGCTAGCTCGC
TAGCTCGATCTTCTCGATCGCGGCTAGGAGAGCTCGAGCTTCGAGGCTGCGAGGATCGCGGAGAGG
AGGATCGAGATCGGATAGAGATCGCGCTAGCTCGATCGCGCGCTAGATTATATATATATTAGCGGC
GCGATAGCTCGCTAGCTGCTAGCTCGCTAGCTCGATCTTCTCGATCGCGGCTAGGAGAGCTCGAGC
TTCGAGGCTGCGAGGATCGCGGAGAGGAGGATCGAGATCGGATCGAGAGCTATAGCGATCGATCGG
ATCGATCGGGATCTTAGCGAAAAGCTCGATTTAGCTAGCTAAAAAAAAAATTTTTTGGGGGCGAGA
TCGATCGATCGATCGCGCTTAGGAAATTCCCCCGCGCGCGGCCCCCGAGATAGGGATAGGATAGGG
ATAGAGATCGCGCTAGCTCGATCGCGCGCTAGATTATATATATATTAGCGGCGCGATAGCTCGCTA
GCTGCTAGCTCGCTAGCTCGATCTTC

[download]
Which outputs 
0  HASH(0x1824334)
   'A' => 535
   'AA' => 84
   'AAA' => 66
   'AAG' => 6
   'AAT' => 12
   'AG' => 223
   'AGA' => 64
   'AGC' => 105
   'AGG' => 54
   'AT' => 228
   'ATA' => 81
   'ATC' => 111
   'ATT' => 36
   'C' => 504
   'CC' => 48
   'CCC' => 36
   'CCG' => 12
   'CG' => 286
   'CGA' => 124
   'CGC' => 117
   'CGG' => 45
   'CT' => 169
   'CTA' => 69
   'CTC' => 54
   'CTG' => 19
   'CTT' => 27
   'G' => 675
   'GA' => 264
   'GAA' => 12
   'GAG' => 87
   'GAT' => 165
   'GC' => 270
   'GCC' => 6
   'GCG' => 117
   'GCT' => 147
   'GG' => 141
   'GGA' => 72
   'GGC' => 33
   'GGG' => 36
   'T' => 490
   'TA' => 186
   'TAA' => 6
   'TAG' => 129
   'TAT' => 51
   'TC' => 186
   'TCC' => 6
   'TCG' => 157
   'TCT' => 22
   'TG' => 25
   'TGA' => 4
   'TGC' => 15
   'TGG' => 6
   'TT' => 93
   'TTA' => 36
   'TTC' => 21
   'TTG' => 6
   'TTT' => 30

[download]

Hope that helps

-InjunJoel
"I do not feel obliged to believe that the same God who endowed us with sense, reason and intellect has intended us to forego their use." -Galileo

In reply to Re: Question about speeding a regexp count by injunjoel
in thread Question about speeding a regexp count by Commander Salamander

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