## what is the general equation for this series / pattern? [closed]

  for an arbitrary word, how can we derive "i" given the pattern below?

for a (i = 1)
a

for ab (i = 3)
a
ab
b

for abc (i = 6)
a
ab
abc
b
bc
c

for abcd (i = 10)
a
ab
abc
abcd
b
bc
bcd
c
cd
d

for abcde (i = 15)
a
ab
abc
abcd
abcde
b
bc
bcd
bcde
c
cd
cde
d
de
e

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 This question is out of the MO scope. Please see the FAQ for a list of other websites where you can ask this question. – David Roberts Nov 25 2011 at 5:26 I'd agree this questions is off topic but it's worth reminding people about the Encyclopedia of Integer Sequences at oeis.org – Jeff Burdges Nov 25 2011 at 5:30 @Jeff - yes. 'Twill provide an easy answer. – David Roberts Nov 25 2011 at 5:32