Mining dictionary for sed search strings - awk

Question

For fun I was mining the dictionary for words that sed could use to modify strings. Example:
sed settee <<< better
sed statement <<< dated
Outputs:
beer
demented
These sed swords must be at least 5 letters long, and begin with s, then another letter, which can appear only 3 times, with at least one other letter between the first and second instances, and with the third instance as the final letter.
I used sed to generate a word list, and it seems to work:
d=/usr/share/dict/american-english
sed -n '/^s\([a-z]\)\(.*\1\)\{2\}$/{
/^s\([a-z]\)\(.*\1\)\{3\}$/!{/^s\([a-z]\)\1/!p}}' $d |
xargs echo
Output:
sanatoria sanitaria sarcomata savanna secede secrete secretive segregate selective selvedge sentence sentience sentimentalize septette sequence serenade serene serpentine serviceable serviette settee severance severe sewerage sextette stateliest statement stealthiest stoutest straightest straightjacket straitjacket strategist streetlight stretchiest strictest structuralist
But that sed code runs three passes through each line, which seems excessively long and kludgy. How can that code be simplified, while still outputting the same word list?
grep or awk answers would also be OK.

Answer 1

awk to the rescue!
code is cleaner with awk and reads as the spec: split the word based on the second char, three instances of the char will split the word into 4 segments; 2nd one should have at least one char and the last one should be empty.
$ awk '/^s/{n=split($1,a,substr($1,2,1));
if(n==4 && length(a[2])>0 && a[4]=="") print}' /usr/share/dict/american-english | xargs
sanatoria sanitaria sarcomata savanna secede secrete secretive
segregate selective selvedge sentence sentience sentimentalize
septette sequence serenade serene serpentine serviceable serviette
settee severance severe sewerage sextette stateliest statement
stealthiest stoutest straightest straightjacket straitjacket strategist
streetlight stretchiest strictest structuralist

Answer 2

very cool idea. I think you're more restrictive than necessary
sed -nE '/^s(.)[^\1]+\1[^\1]*\1g?$/p'
seems to work fine. It generated 518 words for me. I only have /usr/share/dict/words dictionary file though.
sabadilla sabakha sabana sabbatia sabdariffa sacatra saccharilla
saccharogalactorrhea saccharorrhea saccharosuria saccharuria sacralgia
sacraria sacrcraria sacrocoxalgia sadhaka sadhana sahara saintpaulia
salaceta salada salagrama salamandra saltarella salutatoria
...
stuntist subbureau sucuriu sucuruju sulphurou surucucu
syenite-porphyry symphyseotomy symphysiotomy symphysotomy symphysy
symphytically syndactyly synonymity synonymously synonymy
syzygetically syzygy
an interesting find is
$ sed snow-nodding <<< now-or-never
noddior-never

Answer 3

A speedy pcregrep method, (.025 seconds user time):
d=/usr/share/dict/american-english
pcregrep '^s(.)((?!\1).)+\1((?!\1).)*\1$' $d | xargs echo
Output:
sanatoria sanitaria sarcomata savanna secede secrete secretive segregate selective selvedge sentence sentience sentimentalize septette sequence serenade serene serpentine serviceable serviette settee severance severe sewerage sextette stateliest statement stealthiest stoutest straightest straightjacket straitjacket strategist streetlight stretchiest strictest structuralist
Code inspired by: Regex: Match everything except backreference