NB. Interesting, I must have not transcribed the rules.
   NB. You knew this long ago.

   sub_string_count_dwl=: (mp|.)@:>:@:#
   sub_string_count_rh=: {:@:(+/\)@:>:@:i.@:#

   sub_string_count_rh 'abcd'
10

   sub_string_count_dwl 'abcd'
25

   #@:;: 'a b c d ab bc cd abc bcd abcd'
10
   
Reference:
Date: Thu, 10 Jan 2013 11:10:14 -0800
From: Roger Hui <rogerhui.can...@gmail.com>
To: Programming forum <programm...@jsoftware.com>
Subject: Re: [Jprogramming] Contests & Hackatons
Message-ID:
        <CAMZ_i_AKUL
++Ha3u5rRS54J7J8Z4GQuSaGSnrTnJR=4w5xe...@mail.gmail.com>

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